Answer:
The null hypothesis is rejected (P-value=0.0 28).
There is enough evidence to support the claim that that Company A tires outlast the tires of Company B by more than 10,000 miles.
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that that Company A tires outlast the tires of Company B by more than 10,000 miles.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=10000\\\\H_a:\mu_1-\mu_2> 10000[/tex]
being μ1: average for Company A and μ2: average for Company B.
The significance level is 0.05.
The sample 1, of size n1=16 has a mean of 63,500 and a standard deviation of 4,000.
The sample 1, of size n1=12 has a mean of 49,500 and a standard deviation of 6,000.
The difference between sample means is Md=14,000.
[tex]M_d=M_1-M_2=63500-49500=14000[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{4000^2}{16}+\dfrac{6000^2}{12}}\\\\\\s_{M_d}=\sqrt{1000000+3000000}=\sqrt{4000000}=2000[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{14000-10000}{2000}=\dfrac{4000}{2000}=2[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-1=16+12-2=26[/tex]
This test is a right-tailed test, with 26 degrees of freedom and t=2, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t>2)=0.028[/tex]
As the P-value (0.028) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that that Company A tires outlast the tires of Company B by more than 10,000 miles.
In statistics, you can use a two-sample t-test to compare the lifespans of two types of tires. After setting up the null and alternative hypotheses, we use the alpha level, test statistic, and p-value to decide whether to reject the null hypothesis and accept the company's claim.
To clarify, testing this claim about tire lifespan falls under the category of hypothesis testing within statistics. In your case, you're comparing the lifespan of two types of tires which involves a two-sample t-test. Unfortunately, you've only provided raw data, but let's tackle this conceptually.
First, we set up the null and alternative hypotheses. The null hypothesis, usually denoted as H0, asserts that there's no difference between the means of the two populations. In this case, it says the lifespan of Company A's tires are the same as Company B's tires.
The alternative hypothesis, usually denoted as Ha, is the claim you're trying to test - in this case, that Company A's tires do last 10,000 miles longer than Company B's tires. In this hypothesis test, your alpha, which is the threshold of how much you're willing to be wrong, is 0.05.
After calculating the t-score and finding the p-value using statistical software or a t-distribution table, you compare the p-value to the alpha. If the p-value is less than the alpha, that means the result is statistically significant and thus you reject the null hypothesis.
Based on the decision and reason provided in your question, the conclusion would be that there is sufficient evidence at the 0.05 level to support the claim that Company A's tires outlast Company B's tires by more than 10,000 miles.
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There are 3 paper clips and 5 erasers in a paper stack. If 2 items are drawn at random without replacement what is the probability that one draw a paper clip and then an eraser?
Answer:
15/56
Step-by-step explanation:
Total = 8
3/8 × 5/7
15/56
What is the common difference in the following arithmetic sequence?
7,3,-1,-5
Answer:
-4
Step-by-step explanation:
Each term is 4 less than the term before it, so the common difference is -4.
Answer:
B. -4 on edge !!
Step-by-step explanation:
Got it right :)
The design of a concrete mix requires 2,314 lb/yd3 of gravel having a moisture content of 3.5% and absorption of 4.2%, and 899 lb/yd3 of sand having a moisture content of 5.7% and absorption of 1.4%, and 244 lb/yd3 of free water. What is the weight of the mixing water per cubic yard that should be used at the job site?
Answer:
Weight of mixing water=224.541 lb
Step-by-step explanation:
Taking 1 cubic yard of concrete
Mass of gravel = 2314 lb
Moisture content = 3.5% Absorption 4.2%
Extra water needed = (4.2-3.5)*2314/100= 16.198 lb
Mass of sand= 899 lb
Moisture content = 5.7% Absorption =1.4%
Water released = (5.7-1.4)*899/100= 38.657 lb
Free water = 244 lb
Weight of mixing water = free water + extra water needed-water released = 244+16.198-38.657=224.541 lb
Weight of mixing water=224.541 lb
n a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2472 subjects randomly selected from an online group involved with ears. 1022 surveys were returned. Construct a 99% confidence interval for the proportion of returned surveys.
Answer:
0.3876<p<0.4389
Step-by-step explanation:
-Given [tex]n=2472, \ x=1022 , \ CI=0.99[/tex]
-We calculate the proportion of surveys returned:
[tex]\hat p=\frac{1022}{2472}\\\\=0.4134[/tex]
For a 99% confidence interval:
[tex]z_{\alpha/2}=2.576[/tex]
#The margin of error is calculated as;
[tex]ME=z_{0.005}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=2.576\times \sqrt{\frac{0.4134(1-0.4134)}{2472}}\\\\=0.0255[/tex]
The confidence interval are then:
[tex]CI=\hat p\pm ME\\\\=0.4134\pm 0.0255\\\\=[0.3876,0.4389][/tex]
Hence, the confidence interval is 0.3876<p<0.4389
Consider the exponential function
g(x)=190,000•1.03x, which models the value of Evie’s house, where x represents the number of years since she purchased the house.
What is the value of Evie’s house after 5 years rounded to the nearest dollar?
Answer:
$220262
Step-by-step explanation:
We are given that an exponential function
[tex]g(x)=190000\cdot(1.03)^x[/tex]
Where x=Number of years
We have to find the value of Evie's house after 5 years .
Substitute the values in the given function
[tex]g(5)=190000\cdot(1.03)^5[/tex]
[tex]g(5)=220262.07[/tex]
[tex]g(5)\approx 220262[/tex]
Hence, the value of Evie's house after 5 years=$220262
here are the ingredients needed to make 8 pancakes
250ml milk
1 egg
140 g flour
5 g butter
a) simon makes 4 pancakes
workout how much milk he needs
b) craig makes 12 pancakes
workout how much butter he needs
To calculate milk needed for a different number of pancakes and determine the amount of butter for a varied pancake quantity.
To calculate the amount of milk needed for 4 pancakes that Simon is making:
Divide the amount of milk needed for 8 pancakes (250ml) by 2 since 4 is half of 8. 250ml ÷ 2 = 125ml.
To determine the amount of butter for the 12 pancakes that Craig is making:
Since the recipe calls for 5g of butter for 8 pancakes, we can calculate the amount needed for 12 pancakes by setting up a proportion: (5g/8 pancakes) = (x/12 pancakes). Solving for x gives x = 7.5g.
An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 270 cars, they found a mean MPG of 27.8. Assume the variance is known to be 6.25. A level of significance of 0.02 will be used. Make a decision to reject or fail to reject the null hypothesis. Make a decision.
Answer:
The calculated value z = 1.3145 < 2.326 at 0.02 level of significance
The null hypothesis is accepted
Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.
Step-by-step explanation:
Step(i):-
An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.
The mean of the Population 'μ' = 28.0miles/gallon
Given data after testing 270 cars, they found a mean MPG of 27.8. Assume the variance is known to be 6.25.
The sample size 'n' = 270
Mean of the sample 'x⁻' = 27.8
Given Population variance 'σ² = 6.25
The standard deviation of Population 'σ' = √6.25 = 2.5
Step(ii):-
Null hypothesis :H₀: 'μ' = 28.
Alternative hypothesis :H₁: 'μ' ≠28.
The test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{27.8-28 }{\frac{2.5}{\sqrt{270} } } = \frac{-0.2}{0.15214}[/tex]
Z = -1.3145
|Z| = |-1.3145|= 1.3145
Step(iii):-
The tabulated value of z-score at 0.02 level of significance = 2.326
The calculated value z = 1.3145 < 2.326 at a t 0.02 level of significance
The null hypothesis is accepted
Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.
what is the equation of the horizontal line that passes through ( 2 -2 )
Answer:
y = -2
Step-by-step explanation:
The equation of a horizontal line is ...
y = constant
In order to make it go through a point with a y-coordinate of -2, the value of the constant must be -2.
Your line is y = -2.
Uni made a model of a 1970 Ford Mustang using a scale of .5 inches = 9 in. If the actual car is 15 ft long, how long is the model car?
Answer:
The model car is 10 inches long
Step-by-step explanation:
To solve this question, we use conversion of units
Feet to inches.
Each feet has 12 inches.
The car is 15ft long.
So the car has 15*12 = 180 inches.
.5 inches = 9 in.
Rule of three
.5 inches - 9 inches
x inches - 180 inches
[tex]9x = 180*0.5[/tex]
[tex]9x = 90[/tex]
[tex]x = \frac{90}{9}[/tex]
[tex]x = 10[/tex]
The model car is 10 inches long
To find the length of Uni's model car, we convert the actual car's length to inches, set up a proportion with the given scale, and cross-multiply to solve for the model car's length, resulting in a model that is 10 inches long.
The subject matter of the question is related to scale models, which falls under the field of Mathematics. To solve this problem, we need to find the length of the model car based on the given scale and the actual length of the car.
The scale given is 0.5 inches = 9 inches. Firstly, we need to convert the actual length of the car from feet to inches, so we can work in the same units. There are 12 inches in a foot, so a 15 feet long car is 15 x 12 inches long, which is 180 inches. Now, we need to set up a proportion to find the length of the model car:
Actual car length (inch) : Model car length (inch) = Actual scale (inch) : Model scale (inch) 180 inches (actual car length) : x inches (model car length) = 9 inches (actual scale) : 0.5 inches (model scale)
By cross-multiplying, we get:
(180 inches x 0.5 inches) = (x inches x 9 inches)
Dividing both sides by 9 inches, we get:
x inches = (180 inches x 0.5 inches) / 9 inches
So, the length of the model car is:
x inches = 10 inches.
Therefore, Uni's model car is 10 inches long.
Which expression(s) have a greatest common factor (GCF) of 3xy2 with 42xy4
Final answer:
None of the provided expressions have a greatest common factor of 3xy² with 42xy⁴ because they do not contain the necessary factors of 3, x, and y².
Explanation:
The student is asking for expressions that have a greatest common factor (GCF) of 3xy² with 42xy⁴. To find expressions with a GCF of 3xy², we need to look for expressions that include multiples of 3xy² in their factorization.
Looking at the provided expressions:
8ry (2x-1) does not have a GCF of 3xy² because it does not contain the necessary factors of 3 and y².3y similarly lacks x and has only y to the first power, not y².6(22-1) provided also does not contain the full factor of 3xy².4xp(y-2) has the x and p factors, but not 3y².The expression 3(4) simply equals 12, which is not a multiple of 3xy².None of the remaining provided expressions contain the necessary factors of 3xy² either.Therefore, none of the provided expressions have a GCF of 3xy² with 42xy⁴.
What is 1/3x1/3x1/3[/tex]?
Answer:
i believe the answer is 1/27
Step-by-step explanation:
you take the fractions and multiply them all together.
1x1x1 equals 1
and 3x3x3 equals 27
meaning the answer is 1/27 :)
To calculate 1/3 x 1/3 x 1/3, you're effectively cubing 1/3, which results in (1/3)^3 or 1^3/3^3, simplifying to 1/27.
Explanation:The student is asking about the multiplication of fractions and exponentiation rules in algebra. To solve 1/3 x 1/3 x 1/3, you multiply the fractions normally. When multiplying identical fractions, we simply raise the fraction to the power of the number of times it is being multiplied by itself. So 1/3 x 1/3 x 1/3 is equivalent to (1/3)^3. When you raise a fraction to an exponent, you raise both the numerator and the denominator to that power. Therefore, (1/3)^3 equals 1^3/3^3, which simplifies to 1/27.
The example given with 3².35 relates to the rules of exponents, which state that when multiplying exponential terms with the same base, you can add the exponents (x^p x x^q = x^(p+q)). For the concept of cubing of exponentials, you would cube the base and multiply the existing exponent by 3 to execute the operation effectively.
A major home improvement store conducted its biggest brand recognition campaign in the company's history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot". A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad (i.e.. if there is evidence that the population proportion of "like the ads a lot" for the company's ads is less than 0.22) at a 0.01 level of significance. Referring to the above, the null hypothesis will be rejected if the test statistic is:
The null hypothesis will be rejected if the test statistic is: greater than -2.33
The null hypothesis will be rejected if the test statistic falls within the critical region, which is determined by the significance level (0.01 in this case).
To determine the test statistic, calculate the z-score for the sample proportion and compare it to the critical value.
The formula to calculate the z-score for the sample proportion is:
[tex]z = (\hat{p} - p) / \sqrt(p * (1 - p) / n)[/tex]
Where:
[tex]\hat{p}[/tex] is the sample proportion (230/1189 = 0.193)
p is the population proportion (0.22)
n is the sample size (1189)
Calculating the z-score:
z = (0.193 - 0.22) / [tex]\sqrt[/tex](0.22 * (1 - 0.22) / 1189)
z = -2.25
To determine if the null hypothesis is rejected or not, compare the absolute value of the z-score to the critical value for a one-tailed test at a 0.01 significance level.
The critical value for a one-tailed test at a 0.01 significance level is approximately -2.33.
If the absolute value of the calculated z-score is greater than 2.33, we reject the null hypothesis.
Since absolute value of the calculated z-score is not greater than 2.33, null hypothesis is not rejected.
A bag contains 3 white balls, 4 green balls, and 5 red balls. A ball is drawn at random. How many total number of outcomes are there?
Answer:
12.
Step-by-step explanation:
Given that,
Number of while balls are 3
Number of green balls are 4
Number of red balls are 5
We need to find the total number of outcomes. We know the total number of outcomes in is number of choices.
In this case, total number of outcomes are the sum of all color balls i.e. 3 + 4 + 5 = 12 balls.
Hence, the total number of outcomes are 12.
Final answer:
The total number of outcomes when one ball is drawn at random from a bag containing 3 white, 4 green, and 5 red balls is 12.
Explanation:
A bag contains 3 white balls, 4 green balls, and 5 red balls. The total number of possible outcomes when a ball is drawn at random is simply the sum of all the balls in the bag. Since each ball can be selected in one distinct way, we calculate the total number of outcomes by adding the number of white balls, the number of green balls, and the number of red balls.
So, the total number of outcomes is:
3 (white) + 4 (green) + 5 (red) = 12 (total outcomes)
Therefore, there are 12 different possible outcomes when one ball is drawn at random from this bag.
True or False: The megaspore that develops into the megagametophyte leaves the flower when it
reaches maturity
Answer: gang in la
Step-by-step explanation:
The Movie Haven is planning to order new medium-size popcorn containers. It has a choice of four different containers. It costs the company $0.02 per cubic inch of popcorn to fill a container. The company does not want the new container to cost more than $3.00 to fill. Which container should the company use? Use 3.14 for Pi.
Answer:
the answer is container c
b=11.14in2
12in
Step-by-step explanation:
Answer:
Answer is C
Step-by-step explanation:
Reina is buying a house either with brick or with siding, with 1 floor or with 2 floors, and in the city, the suburbs, or the
country. On top of that she can choose from 6 different interior paints and 9 different exterior paints.
Using the fundamental counting principle, simplify the expression
combinations
to determine the number of possible
There are possible combinations.
Reina decides she definitely wants a brick house with one floor. Now the number of possible combinations is
Answer:
1. There are 648 total combinations that can be chosen.
2. After she choses two possiblilities the total number changes to 108 total posibilities to chose from
Step-by-step explanation:
possibility: 1/2 x 1/3 x 1/2 x 1/6 x 1/9 = 648
then you remove the first two because she chose those ones
1/2 x 1/6 x 1/9 = 108 possibilities left
Answer:
Step-by-step explanation:
1. C
2. C
3. B
Ten years ago, college students spent an average of 120 hours per semester on extra-curricular activities. A researcher believes that now college students spend less time on extra-curricular activities than they did ten years ago. A simple random sample of 100 college students found that in the past year the average number of hours spent per semester in extracurricular activities was 107 hours with a standard deviation of 45 hours. If we are testing at a significance level of 0.05, based on the p-value, what is your conclusion?
Answer:
We conclude that the college students spend less time on extra-curricular activities than they did ten years ago.
Step-by-step explanation:
We are given that Ten years ago, college students spent an average of 120 hours per semester on extra-curricular activities.
A simple random sample of 100 college students found that in the past year the average number of hours spent per semester in extracurricular activities was 107 hours with a standard deviation of 45 hours.
Let [tex]\mu[/tex] = average time spent on extra-curricular activities.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 120 hours {means that the college students spend more or equal time on extra-curricular activities than they did ten years ago}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 120 hours {means that the college students spend less time on extra-curricular activities than they did ten years ago}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average number of hours spent per semester = 107 hrs
s = sample standard deviation = 45 hours
n = sample of college students = 100
So, test statistics = [tex]\frac{107-120}{\frac{45}{\sqrt{100} } }[/tex] ~ [tex]t_9_9[/tex]
= -2.889
The value of t test statistics is -2.889.
Now, the P-value of the test statistics is given by following formula;
P-value = P( [tex]t_9_9[/tex] < -2.889) = 0.00314
Since, the P-value is less than the level of significance as 0.05 > 0.00314, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the college students spend less time on extra-curricular activities than they did ten years ago.
Which shapes can the shaded area be divided into to find the area?
O
a rectangle and a triangle
a rectangle and a square
a trapezoid and a rectangle
a trapezoid and two triangles
Answer:
A rectangle and a triangle
Step-by-step explanation:
A woman is emptying her aquarium at a steady rate with a small pump. The water pumped to a 12-in.-diameter cylindrical bucket, and its depth is increasing at the rate of 4.0 in. per minute. Find the rate at which the aquarium water level is dropping if the aquarium measures 24 in. (wide) × 36 in. (long) × 18 in. (high).
Answer:
Therefore the rate at which water level is dropping is [tex]\frac{11}{21}[/tex] in per minute.
Step-by-step explanation:
Given that,
The diameter of cylindrical bucket = 12 in.
Depth is increasing at the rate of = 4.0 in per minutes.
i.e [tex]\frac{dh_1}{dt}=4[/tex]
[tex]h_1[/tex] is depth of the bucket.
The volume of the bucket is V = [tex]\pi r^2 h[/tex]
[tex]=\pi \times 6^2\itimes h_1[/tex]
[tex]\therefore V=36\pi h_1[/tex]
Differentiating with respect yo t,
[tex]\frac{dV}{dt}=36\pi \frac{dh_1}{dt}[/tex]
Putting [tex]\frac{dh_1}{dt}=4[/tex]
[tex]\therefore\frac{dV}{dt}=36\pi\times 4[/tex]
The rate of volume change of the bucket = The rate of volume change of the aquarium .
Given that,The aquarium measures 24 in × 36 in × 18 in.
When the water pumped out from the aquarium, the depth of the aquarium only changed.
Consider h be height of the aquarium.
The volume of the aquarium is V= ( 24× 36 ×h)
V= 24× 36 ×h
Differentiating with respect to t
[tex]\frac{dV}{dt}=24\times 36 \times \frac{dh}{dt}[/tex]
Putting [tex]\frac{dV}{dt}=36\pi\times 4[/tex]
[tex]36\pi\times 4= 24\times 36\times \frac{dh}{dt}[/tex]
[tex]\Rightarrow \frac{dh}{dt}=\frac{36\pi \times 4}{24\times 36}[/tex]
[tex]\Rightarrow \frac{dh}{dt}=\frac{11}{21}[/tex]
Therefore the rate at which water level is dropping is [tex]\frac{11}{21}[/tex] in per minute.
To find the rate at which the aquarium water level is dropping, calculate the volume of water being pumped into the bucket per minute and the volume of the aquarium. Then, divide the volume of water by the volume of the aquarium to find the rate.
Explanation:To find the rate at which the aquarium water level is dropping, we first need to determine the flow rate of water being pumped into the cylindrical bucket.
Now, let's find the rate at which the aquarium water level is dropping:
By calculating the above expression, you can find the rate at which the aquarium water level is dropping.
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The water level in the aquarium is dropping at an average rate of π/6 inches per minute. This is obtained by relating the volumes and their rates of change in both the bucket and the aquarium.
Explanation:The subject of this question is calculus, specifically, related rates. The situation describes two rates: one at which the depth of water in the bucket is increasing, and one at which the water level in the aquarium is dropping - a classic related rates problem.
To comprehend this, let us calculate the volume rates of each one: the bucket and the aquarium. The bucket is referred as cylindrical with a radius of 6 inches (half of 12 inches). The volume of a cylinder is V = πr²h. The depth or height, h, is increasing at the rate of 4 inches per minute, so dh/dt = 4 in/min. The rate at which the volume has been changing, dV/dt = πr²dh/dt = π * (6 in)² * 4 in/min = 144π in³/min.
The aquarium is a rectangular prism, thus its volume can be calculated by V = l*w*h. Therefore, the rate at which the water level is dropping is dV/dt / (l*w) which equals 144π in³/min divided by the area of the aquarium (24in*36in = 864 in²), which gives dh/dt = 144π / 864, which reduces to dh/dt = π/6 in/min downwards. Hence, the water level in the aquarium is dropping at π/6 in/min on an average.
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solve this system using a systems of equations. Discount Rental Cars charges a daily fee plus a mileage fee for renting its cars. Barney was charge 145.00 for 3 days and 310 miles, while Mary was charge 250.00 for 5 days and 600 miles. What does discount Rental Cars charge per day and mile?
Answer:
Barney 145 3 Days 310 Miles
Mary 250 5 Days 600 Miles
A) 3 D + 310 M = 145
B) 5 D + 600 M = 250
Multiplying A) by -5/3
A) -5 D - 516.6666M = -241.66666666
B) 5D + 600M = 250
Adding A) and B)
83.3333 M = 8.3333333333
M = .10 per mile
3 D = 114
Daily Rate = 38 dollars per day
Step-by-step explanation:
Let X denote the courtship time for a randomly selected female-male pair of mating scorpion flies (time from the beginning of interaction until mating). Suppose the mean value of X is 120 min and the standard deviation of X is 110 min (suggested by data in the article "Should I Stay or Should I Go? Condition- and Status-Dependent Courtship Decisions in the Scorpion Fly Panorpa Cognate"†).
The question is a college-level mathematics problem focusing on statistics related to normal distribution, particularly the calculation of probabilities, defining a random variable, and understanding hypothesis testing and p-values.
Explanation:The student's question pertains to the concept of normal distribution and statistics as applied to biological data. Specifically, it involves analysis using the mean and standard deviation of a dataset, and proper understanding of hypothesis testing and p-values in scientific research.
Understanding the Random Variable X
The random variable X, in this context, represents the duration of criminal trials. The question requires defining X and calculating related probabilities using the normal distribution properties. A probability statement and sketching of the graph would aid in visual understanding of the probabilities in question.
In statistical hypothesis testing, a p-value less than the level of significance (e.g., 0.01) typically leads to rejection of the null hypothesis, indicating evidence supporting the alternative hypothesis. The data on fruit flies' fecundity and genetic traits provided is an example of such an analysis.
The Highway Safety Department wants to study the driving habits of individuals. A sample of 37 cars traveling on a particular stretch of highway revealed an average speed of 70.7 miles per hour with a standard deviation of 6.3 miles per hour. Round to 4 decimal places. 1.Calculate a 90% confidence interval for the true mean speed of all cars on this particular stretch of highway
Answer:
90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].
Step-by-step explanation:
We are given that a sample of 37 cars traveling on a particular stretch of highway revealed an average speed of 70.7 miles per hour with a standard deviation of 6.3 miles per hour.
Firstly, the pivotal quantity for 90% confidence interval for the true mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average speed of cars = 70.7 miles per hour
s = sample standard deviation = 6.3 miles per hour
n = sample of cars = 37
[tex]\mu[/tex] = true mean speed
Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.
So, 90% confidence interval for the true mean, [tex]\mu[/tex] is ;
P(-1.688 < [tex]t_3_6[/tex] < 1.688) = 0.90 {As the critical value of t at 36 degree of
freedom are -1.688 & 1.688 with P = 5%}
P(-1.688 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.688) = 0.90
P( [tex]-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90
P( [tex]\bar X-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90
90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]70.7-1.688 \times {\frac{6.3}{\sqrt{37} } }[/tex] , [tex]70.7+1.688 \times {\frac{6.3}{\sqrt{37} } }[/tex] ]
= [68.9517 miles per hour , 72.4483 miles per hour]
Therefore, 90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].
The interpretation of the above interval is that we are 90% confident that the true mean speed of all cars will lie between 68.9517 miles per hour and 72.4483 miles per hour.
The minimum length L of a highway sag curve can be computed by where θ 1 is the downhill grade in degrees (θ 1 < 0°), θ 2 is the uphill grade in degrees (θ 2 > 0°), S is the safe stopping distance for a given speed limit, h is the height of the headlights, and α is the alignment of the headlights in degrees. Compute L for a 55-mph speed limit, where and Round your answer to the nearest foot.
Answer:
The answer to the nearest foot is = 15 feet
Step-by-step explanation:
Solution
The first set taken is to Compute L for a 55-mph speed limit
Given that
L =(θ2 -θ1)/200 (h +S Tan ∝) =
= ( u + 5) 336²/200 (1.9 +336 tan 0.7°)
= 9° (336)²/200 (1.9 +336 tan 0.7°) = 14.7652094
= 15 feet { 9° = 9*π/180 = π/20}
Note: Kindly find an attached image for the complete question given and answered
The table shows the results of a poll of 200 randomly selected juniors and seniors who were asked if they attended prom. Find the probability of each of the events.
juniors seniors
yes 28 97
no 56 19
Express your answer as a fraction, using the backslash. Example: 17 would be written as 1/7.
a) P (a junior who did not attend prom)
b) P (did not attend prom | senior)
c) P (junior | attended prom)
Answer:
(a)[tex]\frac{7}{25}[/tex]
(b)[tex]\frac{19}{116}[/tex]
(c)[tex]\frac{28}{125}[/tex]
Step-by-step explanation:
Number of juniors who attended prom,n(J)=28
Number of seniors who attended prom,n(S)=97
Total of those who attended prom=125Number of juniors who did not attend prom,n(J')=56
Number of seniors who did not attend prom,n(S')=19
Total of those who attended prom=75Total Number of students=200(a) P (a junior who did not attend prom)
[tex]P(J')=\frac{56}{200}= \frac{7}{25}[/tex]
(b)
[tex]P(Senior)=\frac{116}{200}[/tex]
[tex]P ($did not attend prom$ | senior)=\frac{\text{P(seniors who did not attend prom)}}{P(Senior)} \\=\frac{19/200}{116/200} \\=\frac{19}{116}[/tex]
(c)P (junior | attended prom)
[tex]P(Senior)=\frac{84}{200}[/tex]
[tex]P (Junior|$ attended prom$)=\frac{\text{P(juniors who attended prom)}}{P(\text{those who attended prom)}} \\=\frac{28/200}{125/200} \\=\frac{28}{125}[/tex]
Answer:
A. P = 7/25
B. P = 19/116
C. P = 28/125
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly this way:
Juniors Seniors Totals
Yes 28 97 125
No 56 19 75
Totals 84 116 200
2. Find the probability of each of the events.
Let's recall that the formula of probability is:
P = Number of favorable outcomes/Total number of possible outcomes
A. P (a junior who did not attend prom)
P = Juniors who did not attend prom/Total number of students surveyed
P = 56/200
P = 7/25 (Diving by 8 numerator and denominator)
B. P (did not attend prom | senior)
P = Seniors who did not attend prom/Total number of seniors surveyed
P = 19/116
C. P (junior | attended prom)
P = Juniors who attend prom/Total number of students attended prom
P = 28/125
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.1-in and a standard deviation of 1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 4.3% or largest 4.3%.
Final answer:
The question involves Mathematics and requires understanding of statistics and normal distribution to find z-scores for designing helmets to fit a specific range of male head breadths, accommodating all except the smallest and largest 4.3%.
Explanation:
The subject of this question is Mathematics, specifically focusing on statistics and the concept of normal distribution. Engineers designing helmets need to consider the breadths of male heads, which are normally distributed with a given mean and standard deviation. The design requirements stipulate that the helmets should fit all men except for those in the extremities of the distribution (smallest 4.3% and largest 4.3%).
To address such a problem, one would typically use the z-score to identify the cutoff points on a standard normal distribution that correspond to these percentages. The z-score represents the number of standard deviations a data point is from the mean. Therefore, the engineers must calculate the z-scores that correspond to the smallest and largest 4.3% of the distribution to determine the range of head breadths the helmets must accommodate.
The director of a radio broadcasting company wants to determine whether the mean length of commercials on his station is equal to 24 seconds. He samples 200 commercials, and finds that the average length of these commercials is 26.3 seconds, with a standard deviation of 7.2 seconds. He uses a significance level of 5%. What is the value of the test statistic?
Answer:
The value of t test statistics is 4.518.
Step-by-step explanation:
We are given that director of a radio broadcasting company wants to determine whether the mean length of commercials on his station is equal to 24 seconds.
He samples 200 commercials, and finds that the average length of these commercials is 26.3 seconds, with a standard deviation of 7.2 seconds.
Let [tex]\mu[/tex] = mean length of commercials on his station.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24 seconds {means that the mean length of commercials on his station is equal to 24 seconds}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 24 seconds {means that the mean length of commercials on his station is different from 24 seconds}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average length of these commercials = 26.3 seconds
s = sample standard deviation = 7.2 seconds
n = sample of commercials = 200
So, test statistics = [tex]\frac{26.3-24}{\frac{7.2}{\sqrt{200} } }[/tex] ~ [tex]t_1_9_9[/tex]
= 4.518
The value of t test statistics is 4.518.
The equation can be used to determine the number of centimeters, y, in a given number of inches, x. The equation was used to fill in the table below. Inches in Centimeters Number of Inches Number of Centimeters 2 5.08 10 25.4 63.5 40 101.6 What value is missing from the table?
Answer:
25 Inches
Step-by-step explanation:
Given the table:
[tex]\left|\begin{array}{c|c|c|c|c}\text{Number of Inches}&2&10&&40\\\text{Number of Centimeters}&5.08&25.04&63.5&101.6\end{array}\right|[/tex]
We want to determine the missing value on the table.
Let the missing value be x.
1 inch = 2.54 cm
x inch = 63.5
Expressing the above as a ratio
[tex]\dfrac{1}{x}=\dfrac{2.54}{63.5} \\$Cross Multiply$\\2.54x=63.5\\$Divide both sides by 2.54$\\x=25 \:Inches[/tex]
Therefore, the missing value is 25.
Answer:
25 Inches
Step-by-step explanation:
hope this helps :))
Solve for x. Write both solutions, separated
by a comma.
5x2 + 2x - 7 = 0
Answer:
it equals 1
Step-by-step explanation:
(5)(2)+2x−7=5
Step 1: Simplify both sides of the equation.
(5)(2)+2x−7=5
10+2x+−7=5
(2x)+(10+−7)=5(Combine Like Terms)
2x+3=5
2x+3=5
Step 2: Subtract 3 from both sides.
2x+3−3=5−3
2x=2
Step 3: Divide both sides by 2.
2x
2
=
2
2
x=1
Question 3
4 pts
(03.05)
What does 7 >-2 indicate about the positions of 7 and -2 on the number line? (4 points)
0
7 is located on the right of -2, and -2 is located on the right of o
0
7 is located on the left of -2, and -2 is located on the right of o
04
7 is located to the right of -2
7 is located on the left of -2
Question 4
4 pts
Answer:
7 is located to the right of -2
Step-by-step explanation:
Larger numbers are to the right on a number line, so the statement that 7 is larger than -2 means ...
7 is located to the right of -2
Find the midpoint of A and B where A has coordinates (2, 4)
and B has coordinates (-3, -9).
Answer:
(-0.5,-2.5)
Step-by-step explanation:
(x1 + x2) / 2 = x midpoint
(y1 + y2) / 2 = y midpoint
x)
2 + -3 = 5
5 / 2 = -0.5
y)
4 + -9 = -5
-5 / 2 = -2.5
= (-0.5, -2.5)
The midpoint of A and B where A has coordinates (2, 4) and B has coordinates (-3, -9) is (-1/2, -5/2)
What is Coordinate Geometry?A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.
We have to find the midpoint of A and B where A has coordinates (2, 4)
and B has coordinates (-3, -9).
Midpoint = (2-3/2, 4-9/2)
=(-1/2, -5/2)
Hence, the midpoint of A and B where A has coordinates (2, 4) and B has coordinates (-3, -9) is (-1/2, -5/2)
To learn more on Coordinate Geometry click:
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