Answer:
y = -14 in simplest form hope this helped
Step-by-step explanation:
A test of H0: p = 0.5 versus Ha: p > 0.5 has the test statistic z = 1.15. Part A: What conclusion can you draw at the 5% significance level? At the 1% significance level? (6 points) Part B: If the alternative hypothesis is Ha: p ≠ 0.5, what conclusion can you draw at the 5% significance level? At the 1% significance level? (4 points)
Answer:
Part A: The null hypothesis failed to be rejected.
Part B: The null hypothesis failed to be rejected.
Step-by-step explanation:
We have an hypothesis test with null and alternative hypothesis H0: p = 0.5 versus Ha: p > 0.5, which has the test statistic z=1.15.
Part A: If the significance level is 0.05, the conclusion depends on the P-value.
If the P-value is below 5%, the null hypothesis is rejected.
The P-value for this right-tailed tes and z=1.15 is:
[tex]P-value=P(z>1.15)=0.125[/tex]
The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis is failed to be rejected.
Part B: In this case, the significance level is 0.01 and, as the alternative hypothesis is defined with an unequal sign, the test is two-tailed.
This changes the way we calculate the P-value, as we need to compute the two tails.
The P-value is:
[tex]P-value=2P(z>1.15)=0.25[/tex]
The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis is failed to be rejected.
Null hypothesis of a sample suggest that there is no statistical relationship exists in a set of provided single observed variable. The null hypothesis is failed to be rejected for both part A and part B of the question.
Given-Using the hypothesis test we have,
[tex]H_o; p=0.5[/tex]
[tex]H_ap>0.5[/tex]
[tex]z=1.15[/tex]
Null hypothesisNull hypothesis of a sample suggest that there is no statistical relationship exists in a set of provided single observed variable.
Part A: The conclusion to draw at the 5% significance level-
In the right tailed test or upper test the p value for the z score can be given form z table which is,
p-value[tex]=0.125[/tex]
Here the p value 0.125 is bigger than the significance level 0.05. Thus the effect is not significant and the null hypothesis is failed to be rejected.
Part B: If the alternative hypothesis is Ha: p ≠ 0.5, the conclusion to draw at the 5% significance level-
Here for the unequal sign 2-test is performed. The p value for the 2-test is,
p- value[tex]=0.25[/tex]
Here the p value 0.25 is bigger than the significance level 0.05. Thus the effect is not significant and the null hypothesis is failed to be rejected.
Hence, the null hypothesis is failed to be rejected for both part A and part B of the question.
For more about the null hypothesis, follow the link below-
https://brainly.com/question/4454077
Which value of x makes x-16=32true?
Answer:
48
Step-by-step explanation:
32+16=48
48-16=32
Answer:
48
Step-by-step explanation:
add 32 and 16 to get 48
Identify the level of measurement of the data, and explain what is wrong with the given calculation. In a survey, the hair colors of respondents are identified as 100 for brown hair comma 200 for blond hair comma 300 for black hair comma and 400 for anything else. The average (mean) is calculated for 604 respondents and the result is 256.1 .
Answer:
This type of data are not measurement of anything , so it is not feasible to calculate their average(Mean)
Step-by-step explanation:T
The data are at the level of measurement that are Nominal
In level of nominal measurement, letters, numeric and alpha-numeric, words, symbols are used to classify data in the example stated.
Now we recall that,
Brown hair = 100,
Blond hair = 200,
Black hair = 300
Anything else = 400
Thus, 100, 200, 300, 400 are used as code numbers for hair colors and does not have any importance to their values numerically.
There is no arithmetic solutions such as average, total which cannot be solved using these numbers.
Therefore the average mean calculated is not feasible
Answer:
The level of measurement of the date is: nominal level of measurement.
Such data are not counts or measures of anything, so it makes no sense to compute their average (mean)
Step-by-step explanation:
The given data are at the nominal level of measurement. Nominal data is not measurable and cannot be ordered as well. It is qualitative in nature and not quantitative. For example this nominal data type can be measured of categorized as yes or no, high or low, mild, moderate or severe, male or female etc. So there is no point of calculating average of such qualitative data and nominal level of measurement deals with qualitative variables.
A certain organization recommends the use of passwords with the following format: consonant commaconsonant, consonant comma vowel comma consonant comma vowel comma consonant comma numberconsonant, vowel, consonant, vowel, consonant, number (for example, prinay 6prinay6). Assume that repeats are allowed. Complete parts (a) and (b). (a) Assuming passwords are not case sensitive, how many such passwords are possible (assume that there are 5 vowels and 21 consonants)?
Answer: (a). Passwords = 48620250
(b). Passwords = 3111696000
Step-by-step explanation:
The question reads that 'A certain organization recommends the use of passwords with the following format':
Consonant, Vowel, Consonant, Consonant, Vowel, Consonant, Number, Number (for example, pinray45).
The number of consonants is 21, the number of vowels is 5 and the numbers are 10 (0 to 9).
Since, there are 21 consonants and 5 vowels and repetition is allowed.
Use the general multiplication rule for each characters in the sequence.
Multiply by 21 consonants, 5 for vowels and 10 for numbers.
Assuming that the passwords are not case sensitive.
i.e. upper case & lower case letters are same.
Thus, the number of possible passwords is:
Passwords = Consonant * Vowel * Consonant * Consonant * Vowel * Consonant * Number * Number
Passwords = 5 x 21 x 21 x 21 x 5 x21 x 10 = 48620250
(b). Assuming that the passwords are case sensitive
Passwords = 10 x 42 x 42 x 42 x 10 x 42 x 10 = 42 x 420³ = 3111696000
cheers i hope this helps!!!!
The total number of possible passwords is 95,887,125,000.
Explanation:To calculate the number of possible passwords, we need to consider the number of choices for each position in the password. In the given format, we have 5 positions for consonants, 2 positions for vowels, and 1 position for a number. Let's break it down:
For the 1st consonant position, we have 21 choices (since there are 21 consonants).
For the 1st vowel position, we have 5 choices (since there are 5 vowels).
For the 2nd consonant position, we have 21 choices.
For the 2nd vowel position, we have 5 choices.
For the 3rd consonant position, we have 21 choices.
For the number position, we have 10 choices (since there are 10 numbers).
For the 4th consonant position, we have 21 choices.
For the 3rd vowel position, we have 5 choices.
For the 5th consonant position, we have 21 choices.
Finally, for the last consonant and the last vowel positions, we have 21 and 5 choices respectively.
To find the total number of possible passwords, we multiply the number of choices for each position:
Total number of passwords = 21 * 5 * 21 * 5 * 21 * 10 * 21 * 5 * 21 * 5 = 95,887,125,000.
David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station.
(a) What is the probability that more than 8 and less than 12 customers pay in cash?
Answer:
0.09312
Step-by-step explanation:
15C9×0.4⁹×0.6⁶ + 15C10×0.4¹⁰×0.6⁵ × 15C11×0.4¹¹×0.6⁴
0.09311963893
Last month, Ginger's hotel ran an occupancy rate of 85%. Her competitive set had 150,000 room nights included within it that were available for sale during that month. During that month, the competitive set sold a total of 115,000 rooms. What was the approximate occupancy rate INDEX last month for Ginger's hotel? Group of answer choices
Answer:
111
Step-by-step explanation:
-The occupancy rate index is calculated using the following formula:
[tex]Index=\frac{Hotel \ OCC}{Competitive \ OCC}\times 100[/tex]
-The Hotel OCC is the property's occupancy rate given as 85%
-The Competitive OCC, is the competitive set's occupancy rate calculated as;
[tex]Occupancy \ Rate=\frac{Room \ Sold}{Rooms \ Available}\\\\\\=\frac{115000}{150000}\\\\=76.67\%[/tex]
-We then substitute to solve for the occupancy rate index:
[tex]Index=\frac{Hotel \ OCC}{Competitive \ OCC}\times 100\\\\=\frac{0.85}{0.7767}\times 100\\\\=110.86\\\approx 111[/tex]
Hence, the occupancy rate index is 111
A waiter served 12 customers at lunch. Then he worked the dinner shift and served 5 new customers per hour. Write an equation that represents the number of customers the waiter served over lunch and dinner. Identify the x and y variables and explain the meaning of the slope and y-intercept.
The question is asking to find an equation of how many customers the waiter served.
Given: 12 customers at lunch; 5 per hour for dinner
Find: number of customers served at lunch AND dinner
We use variables for this, x and y. A general equation is usually y=ax+b, where y is the solution, x is the variable, and a and b are numbers.
Knowing this information, since it is already given that 12 customers were served, the equation turns into y=ax+12
Additionally, since we don't know how many hours she worked, we can use that as a variable. y=5x+12
x=how many hours the waiter worked at dinner
y=overall hours the waiter worked at both lunch and dinner
slope=5, means customers are going up 5 every hour
y-intercept=12, the given/starting point on the y-axis
You wish to determine the effectiveness of taking Omega-3 tablets to lower a person’s cholesterol. To determine this, you collect data on the cholesterol level of 50 individuals before and after a 6-week course of Omega-3 tablets. Which test would determine if this treatment was effective? a. Two-Sample t-test for means b. Two-Sample z-test for means c. Matched-Pairs t-test d. Two-Sample z-test for proportions
Answer:
Option C - Matched-Pairs t-test
Step-by-step explanation:
Looking at the options given,
-Two-Sample t-test for means is used to test the difference (d0) between two population means. A common application is to determine whether the means are equal. This can't apply to the question as it determine if this treatment was effective.
- Two-Sample z-test for means is used to test the null hypothesis that there is no difference between the means of two independent populations. This doesn't determine if this treatment was effective
-Matched-Pairs t-test is used to test whether there is a significant mean difference between two sets of paired data. This will be sufficient to determine if this treatment was effective
-Two-Sample z-test for proportions is used when we want to know whether two populations or groups (e.g., males and females; theists and atheists) differ significantly on some single (categorical) characteristic - for example, whether they are vegetarians. This can't be used to determine if this treatment was effective
The only correct option is Matched-Pairs t-test
To evaluate the effectiveness of Omega-3 tablets for lowering cholesterol, a Matched-Pairs t-test should be used, as it compares the cholesterol levels before and after treatment in the same individuals.
Explanation:To determine the effectiveness of taking Omega-3 tablets to lower a person's cholesterol, one should use a statistical hypothesis test that compares two related samples. In this case, the comparison is between cholesterol levels before and after the 6-week course. Since the same individuals are tested twice, the appropriate test is the Matched-Pairs t-test (also known as the paired sample t-test or dependent sample t-test). This test is utilized when you have two sets of related data and want to assess if their means differ. The differences between each pair will follow a normal distribution if certain conditions are met, which is assumed in a matched-pairs t-test.
Learn more about Matched-Pairs t-test here:https://brainly.com/question/15365572
#SPJ3
The radius of a sphere X is 3 inches, and radius of sphere Y is 9 inches. How many
times larger is the volume of sphere Y compared to sphere X?
The volume of the sphere Y is 27 times the volume of the sphere X
Step-by-step explanation:
Sphere X:
Radius of sphere X = 3 inches
Volume = (4/3) π(27)
Sphere Y:
Radius of sphere Y = 9 inches
Volume = (4/3) π(729)
Volume of sphere Y /volume of sphere X = (4/3) π(729) /(4/3) π(27)
= (729) /(27)
= 27
The volume of the sphere Y is 27 times the volume of the sphere X
In a study conducted to examine the quality of fish after 7 days in ice storage, ten raw fish of the same kind and approximately the same size were caught and prepared for ice storage. The fish were placed in ice storage at different times after being caught. A measure of fish quality was given to each fish after 7 days in ice storage. Review the accompanying sample data and scatterplot, where "Time" is the number of hours after being caught that the fish was placed in ice storage and "Fish Quality" is the measure given to each fish after 7 days in ice storage (higher numbers mean better quality). Is it appropriate to use the correlation coefficient to describe the strength of the relationship between "Time" and "Fish Quality"?
It is appropriate to use the correlation coefficient to describe the strength of the relationship between "Time" and "Fish Quality" in this study. The correlation coefficient measures the strength and direction of the linear relationship between two variables.
Explanation:It is appropriate to use the correlation coefficient to describe the strength of the relationship between "Time" and "Fish Quality" in this study. The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, "Time" and "Fish Quality" are both continuous variables, and a scatterplot can be used to visually represent their relationship.
In the scatterplot, if the data points form a clear pattern or trend, it suggests a strong relationship between the variables. The correlation coefficient quantifies this relationship, ranging from -1 (perfect negative relationship) to 1 (perfect positive relationship), with 0 indicating no linear relationship. By calculating the correlation coefficient, we can determine the strength and direction of the relationship between "Time" and "Fish Quality" in the study.
Keywords: correlation coefficient, relationship, variables, scatterplot, strength, direction, linear, continuous
Learn more about Correlation Coefficient here:https://brainly.com/question/15577278
#SPJ11
6(2x-5y)-2(x+9y) simplified
Answer:
10x-48y
Step-by-step explanation:
The function f(x) = -3x + 200 shows the height in feet of Complete the statements to show the difference in the
a feather dropped from an initial height of 200 feet above mathematical and reasonable domain and range for the
the moon's surface after x seconds.
function. Round any decimals to the nearest integer.
Mathematical range:ys
Reasonable range:
Answer:
Mathematical 200
reasonable 0,200
Step-by-step explanation:
i got it right on the test
Shaun needs to make mortar for brick-laying. It is made in the ratio 7:3 of sand to cement.
If 210 kg of sand is used, how much cement is needed?
mike is flying a kite the horizontal distance to the kite a is about 19 feet the kite is 31 feet from the ground how long is the string
Answer:36.36feet (that rounded but if you want you can round it to 36.4
Step-by-step explanation:
Final answer:
The problem involves using the Pythagorean theorem to find the length of a kite string given the horizontal and vertical distance, which would be the square root of the sum of the squares of 19 feet and 31 feet.
Explanation:
The student's question concerns the length of the string used to fly a kite when given the horizontal distance and the vertical distance from the ground to the kite. To solve this, we apply the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this problem, the kite string functions as the hypotenuse, the horizontal distance to the kite is one leg, and the vertical distance from the ground to the kite is the other leg.
For Mike's kite:
The horizontal distance (leg a) to the kite = 19 feetThe vertical distance (leg b) from the ground to the kite = 31 feetAccording to the Pythagorean theorem:
[tex]\( c^2 = a^2 + b^2 \\( c^2 = 19^2 + 31^2 \\( c^2 = 361 + 961 \\( c^2 = 1322 \\( c = \\( c \\) = \\( c \\) = \\) is the length of the kite string[/tex].
Therefore, Mike's kite string is approximately \\( c \\) long.
Which of the following statements are correct? A. The statement that the random variable X is normally distributed with parameters is often abbreviated . B. If the random variable X is normally distributed with parameters , then . C. The graph of any normal probability density function is symmetric about the mean and bell-shaped, so the center of the bell (point of symmetry) is both the mean of the distribution and the median. D. If the random variable X is normally distributed with parameters , then a large implies that a value of X far from may well be observed, whereas such a value is quite unlikely when is small. E. All of the above statements are correct
Answer:
A. The statement that the random variable X is normally distributed with parameters is often abbreviated.
Step-by-step explanation:
The X is normally distributed with parameters u and is often distributed as X ≈N (u 2 ). The correct answer is a. The statement that the random variable is normally distributed.
The circular base of the cone has a radius of 5 cm. The height of the cone is 12 cm and the slant height is 13 cm. What is approximate surface area of the cone? Use 3.14 as pi and round to the nearest whole number!
Answer: 283cm
Step-by-step explanation:
what is the probability of rolling a dice twice, and having it land on a number greater than 1 both times?
Answer:
25/36
Step-by-step explanation:
P(1) = 1/6
P'(1) = 5/6
5/6 * 5/6 = 25/36
Show a number line to the inequality x-1>2
Answer:
see below
Step-by-step explanation:
x-1>2
Add 1 to each side
x-1+1>2+1
x >3
There would be an open circle at 3 and a line to the right
Jordan spends $9.90 for 5 pounds of apples find the unit cost 7 dollars
Answer:
$1.98/ lbs
Step-by-step explanation:
To find the unit cost, take the total cost and divide the the number of units purchased
$9.90/5 lbs
$1.98/ lbs
In 2017, the entire fleet of light‑duty vehicles sold in the United States by each manufacturer must emit an average of no more than 92 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and non methane organic gas (NMOG) over the useful life ( 150,000 miles of driving) of the vehicle. NOX + NMOG emissions over the useful life for one car model vary Normally with mean 88 mg/mi and standard deviation 4 mg/mi. (a) What is the probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG? (Enter your answer rounded to four decimal places.)
Answer:
0.6915
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 88, \sigma = 4[/ex]
What is the probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG?
This is 1 subtracted by the pvalue of Z when X = 86. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{86 - 88}{4}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a pvalue of 0.3085
1 - 0.3085 = 0.6915
The answer is 0.6915
finding the size of angle x on a straight line. 2 of the angles are 29 degree and 82 degrees
Answer:
x = 111°
Step-by-step explanation:
We know that angles in a triangle add up to 180°
Step 1: Find angle supplementary to x
82 + 29 + x = 180
111 + x = 180
x = 69°
Step 2: Find angle x
Both the angles are supplementary, meaning they add up to 180°.
x + 69 = 180
x = 111°
Answer:
Easy = 111 degrees
Step-by-step explanation:
abby is making a maze for her pet mouse the diameter of the maze is 24 what is the circumference
Answer:
75.36
Step-by-step explanation:
To find the diameter, take the radius and multiply it by two, or use the diameter, and then multiply by pi. The formula, in this case, would be pi x 24. I hope this helps. I used 3.14, the shorter version, but a more precise answer would be 75.3982236862, or 75.4 rounded.
Helena is in charge of selling tickets for the upcoming
play at Willowbrook School. Each drama club member
has been asked to sell tickets to friends and family
members, and Helena wants to know approximately how
many tickets have been sold so far.
Homeroom Data of Tickets Sold:
20, 15, 19, 16, 10
Calculate the mean
Answer:
16
Step-by-step explanation:
You want the mean of {20, 15, 19, 16, 10}.
MeanThe mean is the sum of the numbers, divided by the number of numbers.
(20 +15 +19 +16 +10)/5 = 80/5 = 16
The mean is 16.
Final answer:
The mean of tickets sold by Helena for the Willowbrook School play is calculated by adding the total tickets sold (80) and dividing by the number of homerooms (5), resulting in a mean of 16 tickets.
Explanation:
To calculate the mean of tickets sold for the Willowbrook School play, we need to add up the number of tickets sold in each homeroom and then divide by the number of homerooms. The data given is:
20 tickets15 tickets19 tickets16 tickets10 ticketsAdding these together, we get 20 + 15 + 19 + 16 + 10 = 80 tickets sold in total. As there are 5 sets of data, we divide the total by 5 to find the mean.
Therefore, the mean number of tickets sold is 16 tickets.
Solve 2 + 3ex + 2 = 7 for x.
Answer:
The answer is C. x=In(5/3)-2
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Find the savings plan balance after 18 months with an APR of 2% and monthly payments of $200.
The balance is $ 1
(Do not round until the final answer. Then round to the nearest cent as needed.)
Answer:
$800 [((1.005)18 - 1)/.005]
$800 x [(1.0939 - 1)/.005]
$800 x (0.0939/0.005)
$800 x 18.785
~ $15,028
The savings plan is 15,028.
Step-by-step explanation:
The savings plan balance on the account after 18 months is $3651.46.
What is the balance after 18 months?Basically, the savings plan balance means the total amount of money saved and accumulated in a designated account or investment over a period of time.
The savings plan balance will be found using annuity formula [tex]P * [(1 + r)^n - 1] / r[/tex]
Data:
P = Monthly payment = $200r = Monthly interest rate = 0.02 / 12 = 0.00166667n = Number of months = 18The plan balance will be:
= 200 * [(1 + 0.00166667)^18 - 1] / 0.00166667
= 200 * 18.2572814188
= 3651.45628376
= 3651.46.
Read more about plan balance
brainly.com/question/35585538
#SPJ3
Five samples of a ferrous-type substance are to be used to determine if there is a difference between a laboratory chemical analysis and an X-ray fluorescence analysis of the iron content. Each sample was split into two sub-samples and the two types of analysis were applied. Following are the coded data showing the iron content analysis:
Sample
Analysis 1 2 3 4 5
X-rays 2.0 2.0 2.3 2.1 2.4
Chemical 2.2 1.9 2.5 2.3 2.4
Assuming that the populations are normal, test at the 0.05 level of significance whether the two methods of analysis give, on the average, the same result.
Step-by-step explanation:
Step 1
From the given information,
number of ferrous-type substance, n = 5
Let [tex]\mu_1[/tex] and [tex]\mu_2[/tex] are the true population average for laboratory chemical and X-ray flourescence analysis
Level of significance, [tex]\alpha = 0.05[/tex]
state the null and alternative hypotheses
[tex]H_0 : \mu_1 - \mu_2 = 0\\\\H_1 : \mu_1 - \mu_2 \neq 0[/tex]
Attached are steps 2 to 7 of the remaining solution
Yes, the two methods of analysis give, on average, the same result and this can be determined by using the given data.
Given :
Five samples of a ferrous-type substance are to be used.Each sample was split into two sub-samples and the two types of analysis were applied.0.05 level of significance.The mean of the first sample is:
[tex]\bar{X_1} = \dfrac{\sum X_1}{n_1}[/tex]
[tex]\bar{X_1} = \dfrac{ 10.8}{5}=2.16[/tex]
Now, the standard deviation of the first sample is:
[tex]S_1 =\sqrt{\dfrac{\sum(X_1-\bar{X_1})^2}{n_1-1}}[/tex]
[tex]S_1 =\sqrt{\dfrac{0.132}{4}}=0.182[/tex]
The mean of the second sample is:
[tex]\bar{X_2} = \dfrac{\sum X_2}{n_2}[/tex]
[tex]\bar{X_2} = \dfrac{ 11.3}{5}=2.26[/tex]
Now, the standard deviation of the second sample is:
[tex]S_2 =\sqrt{\dfrac{\sum(X_2-\bar{X_2})^2}{n_2-1}}[/tex]
[tex]S_2 =\sqrt{\dfrac{0.212}{4}}=0.230[/tex]
Now, the hypothesis test is given below:
Null Hypothesis -- [tex]H_0:\mu_1=\mu_2[/tex]
Alternative Hypothesis -- [tex]H_a:\mu_1\neq \mu_2[/tex]
The degree of freedom is calculated as:
[tex]df=n_1+n_2-2\\df=8[/tex]
Now, the formula of the test statistics is given below:
[tex]t = \dfrac{(\bar{X_1}-\bar{X_2})-(\mu_1-\mu_2)}{\sqrt{\dfrac{S^2_1}{n_1}+\dfrac{S^2_2}{n_2}} }[/tex]
[tex]t = \dfrac{2.16-2.26}{\sqrt{\dfrac{(0.182)^2}{5}+\dfrac{(0.230)^2}{5}} }[/tex]
[tex]t = -0.76238688[/tex]
Now, according to the t-value, the p-value is 0.46771. Therefore, the null hypothesis is not rejected.
So, yes the two methods of analysis give, on average, the same result.
For more information, refer to the link given below:
https://brainly.com/question/2695653
orange jelly beans is 82 and that exam scores have an approximately symmetric distribution. She gives orange jelly beans to 25 randomly selected students and finds that these students had a sample mean score of 87 with a sample standard deviation of 10. She wants to have 95% confidence in her result. 27. Conduct a hypothesis test using the confidence interval approach. Write your answer on paper and upload a photo or scan, or else put your answer in an electronic file and upload the file. In order to earn full credit your answer must include all of the following: A statement of the confidence interval in a complete sentence using the appropriate statistical symbol. Include two decimal points in your numbers. The statistical criterion you use to determine whether to reject or fail to reject the hypothesis. The result of your test in statistical terms
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 82
For the alternative hypothesis,
µ ≠ 82
This is a 2 tailed test
Since the sample mean and sample standard deviation is given, the t test would be used to determine the test statistic. The formula is
t = (x - µ)/(s/√n)
Where
x = sample mean = 87
µ = population mean = 82
s = samples standard deviation = 10
n = 25
t = (87 - 82)/(10/√25) = 2.5
α = 1 - Confidence level
α = 1 - 0.95 = 0.05
Since α = 0.05, the critical value is determined from the t distribution table.
For the left, α/2 = 0.05/2 = 0.025
For the right of 0.025 = 1 - 0.025 = 0.975
To determine the t score from the t distribution table, we would find the degree of freedom, df and look for the corresponding α value.
df = n - 1 = 25 - 1 = 24
t score = critical value = ±2.064
In order to reject the null hypothesis, the test statistic must be smaller than - 2.5 or greater than 2.5
Since - 2.064 > - 2.5 and 2.064 < 2.5, we would fail to reject the null hypothesis.
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
Margin of error = z × s/√n
Where
s = sample standard deviation
z = t score
Margin of error = 2.064 × 10/√25
= 4.13
Confidence interval = 87 ± 4.13
the lower limit of this confidence interval is
87 - 4.13 = 82.87
the upper limit of this confidence interval is
87 + 4.13 = 91.13
What is the area of the sector that is not shaded?
Answer:
24
Step-by-step explanation:
cuantas unidades mide el lado QR? cual es la distancia entre los puntos P y R
Answer:
Part A) [tex]QR=2\sqrt{5}\ units[/tex]
Part B) [tex]PR=2\sqrt{13}\ units[/tex]
Step-by-step explanation:
The complete question in English is
Observe the isosceles PQRS trapeze in the Cartesian plane.
A) How long is the QR side?
B) What is the distance between points P and R?
The picture of the question in the attached figure
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Part A) How long is the QR side?
we have the coordinates
Q(7,6) and R(9,2)
substitute in the formula
[tex]d=\sqrt{(2-6)^{2}+(9-7)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(2)^{2}}[/tex]
[tex]d_Q_R=\sqrt{20}\ units[/tex]
simplify
[tex]d_Q_R=2\sqrt{5}\ units[/tex]
Part B) What is the distance between points P and R?
we have the coordinates
P(3,6) and R(9,2)
substitute in the formula
[tex]d=\sqrt{(2-6)^{2}+(9-3)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(6)^{2}}[/tex]
[tex]d_P_R=\sqrt{52}\ units[/tex]
simplify
[tex]d_P_R=2\sqrt{13}\ units[/tex]
You select a marble without looking and then put it back. If you do this 60 times, what is the best prediction possible for the number of times you will pick a blue or a purple marble?
The best prediction for selecting a blue marble 60 times, with replacement, from a bag of 4 blue marbles and 3 white marbles is approximately 34.29 times.
To predict the number of times you will select a blue or purple marble, we need to know the total number of marbles, the number of blue marbles, the number of purple marbles, and the number of trials (which is 60 in this case). Since no information about purple marbles is provided, let's assume you meant blue marbles only for this explanation. In the scenario presented in the question, the probability of drawing a blue marble is 4/7 each time since there are 4 blue marbles and 3 white marbles, totaling 7 marbles.
The probability of drawing a blue marble is 4/7.Each draw is independent because the marble is replaced each time.The predicted number of times a blue marble is drawn in 60 trials is calculated by multiplying the probability by the number of trials which is (4/7) * 60.Therefore, the best prediction for the number of times a blue marble will be selected is approximately 34.29 times (which you might round to 34 times).