Answer:
a) 0.011 = 1.1% probability that the sample mean hardness for a random sample of 17 pins is at least 51
b) 0.0001 = 0.1% probability that the sample mean hardness for a random sample of 45 pins is at least 51
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 50, \sigma = 1.8[/tex]
(a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 17 pins is at least 51?
Here [tex]n = 17, s = \frac{1.8}{\sqrt{17}} = 0.4366[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 51. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{51 - 50}{0.4366}[/tex]
[tex]Z = 2.29[/tex]
[tex]Z = 2.29[/tex] has a pvalue of 0.9890
1 - 0.989 = 0.011
0.011 = 1.1% probability that the sample mean hardness for a random sample of 17 pins is at least 51
(b) What is the (approximate) probability that the sample mean hardness for a random sample of 45 pins is at least 51?
Here [tex]n = 17, s = \frac{1.8}{\sqrt{45}} = 0.2683[/tex]
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{51 - 50}{0.0.2683}[/tex]
[tex]Z = 3.73[/tex]
[tex]Z = 3.73[/tex] has a pvalue of 0.9999
1 - 0.9999 = 0.0001
0.0001 = 0.1% probability that the sample mean hardness for a random sample of 45 pins is at least 51
Final answer:
To find the probability that the sample mean hardness for a random sample of 17 pins is at least 51, we can convert it to a standard normal distribution and use the z-score formula. The probability is approximately 0.011. For a sample size of 45 pins, the probability is approximately 0.001.
Explanation:
To find the probability that the sample mean hardness for a random sample of 17 pins is at least 51, we can convert it to a standard normal distribution and use the z-score formula. The formula for the z-score is:
z = (x - μ) / (σ / sqrt(n))
where x is the value we are interested in (51), μ is the mean (50), σ is the standard deviation (1.8), and n is the sample size (17).
Plugging in the values, we get:
z = (51 - 50) / (1.8 / sqrt(17))
Calculating this, we find that the z-score is approximately 1.044. Looking up this z-score in the z-table, we find that the probability is 0.853. However, we are interested in the probability that the hardness is at least 51, which means we need to find the area to the right of the z-score. So, we subtract the probability from 1:
Probability = 1 - 0.853 = 0.147, or approximately 0.011 when rounded to four decimal places.
Therefore, the probability that the sample mean hardness for a random sample of 17 pins is at least 51 is approximately 0.011.
To find the probability that the sample mean hardness for a random sample of 45 pins is at least 51, we follow the same process. The only difference is that the sample size is now 45 instead of 17. Plugging in the values into the z-score formula, we find that the z-score is approximately 3.106. Looking up this z-score in the z-table, we find that the probability is 0.999. Subtracting this probability from 1, we get:
Probability = 1 - 0.999 = 0.001.
Therefore, the probability that the sample mean hardness for a random sample of 45 pins is at least 51 is approximately 0.001.
A teacher wants to see if a new unit on factoring is helping students learn. She has five randomly selected students take a pre-test and a post test on the material. The scores are out of 20. Has there been improvement? (pre-post) Student 1 2 3 4 5 Pre-test 12 14 11 12 13 Post- Test 15 17 11 13 12 The test statistic equals -1.50 What would be the p-value? Group of answer choices p-value is between 0.01 and 0.025 p-value > 0.20 p-value < 0.002 p-value > 0.10
Answer:
Step-by-step explanation:
Given the sample data
Pre-test... 12 14 11 12 13
Post-Test 15 17 11 13 12
The mean of pre-test
x = ΣX / n
x = (12+14+11+12+13) / 5
x = 12.4
The standard deviation of pre-test
S.D = √Σ(X-x)² / n
S.D = √[(12-12.4)²+(14-12.4)²+(11-12.4)²+(12-12.4)²+(13-12.4)² / 5]
S.D = √(5.2 / 5)
S.D = 1.02.
The mean of post-test
x' = ΣX / n
x' = (15+17+11+13+12) / 5
x' = 13.6
The standard deviation of post-test
S.D' = √Σ(X-x)² / n
S.D' = √[(15-13.6)²+(17-13.6)²+(11-13.6)²+(13-13.6)²+(12-13.6)² / 5]
S.D = √(23.2 / 5)
S.D = 2.15
Test value
t = (sample difference − hypothesized difference) / standard error of the difference
t = [(x-x') - (μ- μ')] / (S.D / n — S.D'/n)
t = (12.4-13.6) - (μ-μ')/ (1.02/5 - 2.15/5)
-1.5 = -1.2 - (μ-μ') / -0.226
-1.5 × -0.226 = -1.2 -(μ-μ')
0.339 = -1.2 - (μ-μ')
(μ-μ') = -1.2 -0.339
μ-μ' = -1.539
Then, μ ≠ μ'
We can calculate our P-value using table.
This is a two-sided test, so the P-value is the combined area in both scores.
The p-value is 0.172
The p value > 0.1
Using the t-distribution, it is found that the p-value is of 0.086.
At the null hypothesis, it is tested if there is no improvement, that is, the subtraction of the mean of the grades on test 1 by the mean of the grades on test 2 is of at least 0, that is:
[tex]H_0: \mu_1 - \mu_2 \geq 0[/tex]
At the alternative hypothesis, it is tested if there is improvement, that is, the grades on the second test were greater than on the first, hence:
[tex]H_1: \mu_1 - \mu_2 < 0[/tex]
We can find the standard deviation for the samples, hence, the t-distribution is used.
The p-value is found using a left-tailed test, as we are testing if the variable is less than a value, with 5 + 5 - 2 = 8 df and t = -1.5, using a calculator, the p-value is of 0.086.
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1/3=n+3/4 what dies n equal??
Use the empirical rule to solve the problem. The annual precipitation for one city is normally distributed with a mean of 288 inches and a standard deviation of 3.7 inches. Fill in the blanks. In 95.44% of the years, the precipitation in this city is between ___ and ___ inches. Round your answers to the nearest tenth as needed.
Answer:
[tex]z=-1.99<\frac{a-288}{3.7}[/tex]
[tex]z=1.99<\frac{a-288}{3.7}[/tex]
And if we solve for a we got
[tex]a=288 -1.99*3.7=214.4[/tex]
[tex]a=288 +1.99*3.7=295.4[/tex]
And the limits for this case are: (214.4; 295.4)
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the annual precipitation of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(288,3.7)[/tex]
Where [tex]\mu=288[/tex] and [tex]\sigma=3.7[/tex]
The confidence level is 95.44 and the signficance is [tex] 1-0.9544=0.0456[/tex] and the value of [tex]\alpha/2 =0.0228[/tex]. And the critical value for this case is [tex]z = \pm 1.99[/tex]
Using this condition we can find the limits
[tex]z=-1.99<\frac{a-288}{3.7}[/tex]
[tex]z=1.99<\frac{a-288}{3.7}[/tex]
And if we solve for a we got
[tex]a=288 -1.99*3.7=214.4[/tex]
[tex]a=288 +1.99*3.7=295.4[/tex]
And the limits for this case are: (214.4; 295.4)
Angles opposite to one another at the intersection of two lines are called ____ angles.
Answer:
A Vertical Angle
Step-by-step explanation:
Answer:
vertical angles
Step-by-step explanation:
Cars on Campus. Statistics students at a community college wonder whether the cars belonging to students are, on average, older than the cars belonging to faculty. They select a random sample of 18 cars in the student parking lot and find the average age to be 8.4 years with a standard deviation of 7.3 years. A random sample of 15 cars in the faculty parking lot have an average age of 4.2 years with a standard deviation of 3.8 years.
1. The null hypothesis is H0:????????=???????? H 0 : μ s = μ f . What is the alternate hypothesis? A. H????:????????≠???????? H A : μ s ≠ μ f B. H????:????????<???????? H A : μ s < μ f C. H????:????????>???????? H A : μ s > μ f
2. Calculate the test statistic. =
3. Calculate the p-value for this hypothesis test. p value =
4. Suppose that students at a nearby university decide to replicate this test. Using the information from the community college, they calculate an effect size of 0.7. Next, they obtain samples from the university student and faculty lots and, using their new sample data, conduct the same hypothesis test. They calculate a p-value of -0.0213 and an effect size of 0.487. Do their results confirm or conflict with the results at the community college? A. It contradicts the community college results because the effect size is much smaller. B. It confirms the community college results because the effect size is nearly the same. C. It contradicts the community college results because the p-value is much bigger D. It can neither confirm or contradict the community college results because we don't know the sample sizes the university students used. E. It confirms the community college results because the p-value is much smaller.
Answer:
Let the 1st group be of students and 2nd group be of faculty.
n1 = 18
\bar{x}_{1} = 8.4
s1 = 7.3
n2 = 15
\bar{x}_{2} = 4.2
s2 = 3.8
1.
H0: =
HA: >
2.
Equality of variance test:
F = s12/s22
= 53.29/14.44
= 3.69
df-num = n1-1 = 17
df-den = n2-1 = 14
p-value = 0..008 < 0.05 i.e.H0 can be rejected and hence we can say that both populations do not have the same variances.
So, test-statistic will be calculated as follows:
[ Find the solution of this part in the attachment]
3.
df = 26
p-value = 0.0217
4.
E. It confirms the community college results because the p-value is much smaller.
pls help!!!!!!!!! if possible will mark brainliest!
Answer:
i think you may have to use sin or cos
Step-by-step explanation:
Answer:
9m (You were correct!!!!)
Step-by-step explanation:
Use Pythagorean Theorem:
[tex]a^{2} +b^{2} = c^{2}[/tex]
⬆️ ⬆️ ⬆️
legs hypotenuse
x² + 12² = 15²
x² + 144 = 225
x² = 81
x = 9
the quoteint of 2 and a number x,times 3
Answer:
just look it up on m..a.t.h. w.a.y.!!
Step-by-step explanation:
it works for me
Which numbers are irrational? Check all that apply.
1.9/15
2. sqrt of 18
3.sqrt of 9
4.sqrt of 169
5.sqrt of 78
6.pi
Answer: B, E, and F
Step-by-step explanation: :)
What is the measure of side x in the isosceles triangle that is shown below
Answer:
x = 29 cm
Step-by-step explanation:
An isosceles triangle has two equal sides that have equal angles at the bases
Since the 80 degree angles are at the bases of the 29 cm side, the length of x must be 29 cm
Answer:
29 cm
Step-by-step explanation:
Because both angles are 80 degrees. If your angles are the same so are your sides.
The slope of a line is 2. The y-intercept of the line is –6. Which statements accurately describe how to graph the function? Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points. Locate the ordered pair (0, –6). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points. Locate the ordered pair (–6, 0). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points. Locate the ordered pair (–6, 0). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
The y-intercept is the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis.
The slope(m) is:
[tex]m=\frac{rise}{run}[/tex]
"rise" is the number of units you go up(+) or down(-) from each point
"run" is the number of units you go to the right from each point
You know:
y-intercept = -6 or (0, -6)
m = 2 or [tex]\frac{2}{1}[/tex] , so from each point you go up 2 units and to the right 1 unit to get to the next point.
#1: Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
This is true
#2: Locate the ordered pair (0, –6). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
This isn't accurate because the slope doesn't move left.
#3: Locate the ordered pair (–6, 0). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
This isn't accurate because (-6, 0) isn't the y-intercept or a point on the y-axis
#4: Locate the ordered pair (–6, 0). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
This isn't accurate because (-6, 0) isn't the y-intercept or a point on the y-axis, and the slope doesn't move to the left.
Answer:
tis be A my friends
Step-by-step explanation:
Antonia is factoring the polynomial, which has four terms.
21x3−63x2+15x−45
3[7x3−21x2+5x−15]
3[7x2(x−3)+5(x−3)]
Which is the completely factored form of her polynomial?
21x2(x − 3)
36x2(x − 3)
3(7x2 + 5) (x − 3)
3(12x2 + 5) (x − 3)
Answer:
3(7x2 + 5) (x − 3) took the quiz :)
Step-by-step explanation:
Answer:
C- 3(7x2 + 5) (x − 3)
Step-by-step explanation:
The equation, y=−16x2+32x+24 , represents the height, in feet, of a firework x seconds after it is launched. What is the maximum height of the firework? Enter your answer in the box. feet
Answer:
40
Step-by-step explanation:
got 100 on quiz
The maximum height of the firework is 40 feet.
What is maximum height?
'The maximum height of the object is the highest vertical position along its trajectory.'
According to the given problem,
y = -16x²+32x+24
For maximum height,
The slope of y with respect to x has to be 0.
⇒ [tex]\frac{dy}{dx}[/tex] = 0
Now, [tex]\frac{d(-16x^{2} +32x+24)}{dx}[/tex] = -32x +32
⇒-32x + 32 = 0
⇒ 32 = 32x
⇒1 = x or x = 1 second
Therefore after 1 second, the firework reaches maximum height.
Now, we put the value of x = 1 second in the equation: y = -16x²+32x+24
⇒ -16(1)² + 32(1) +24
= -16+32+24
= 40 feet
Hence, we can conclude that after 1 second, the firework reaches a maximum height of 40 feet.
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Spam: A researcher reported that 71.8% of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be 69%. He examines a random sample of 500 emails received at an email server, and finds that 365 of the messages are spam. Can you conclude that the percentage of emails that are spam is greater than 69% ? Use both =α0.01 and =α0.05 levels of significance and the P-value method with the TI-84 Plus calculator.
Complete Question:
Spam: A researcher reported that 71.8% of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be 69%. He examines a random sample of 500 emails received at an email server, and finds that 365 of the messages are spam. Can you conclude that greater than 69% of emails are spam? Use both a=0.01 and a=0.05 levels of significance and the -value method with the table.
(a) State the appropriate null and alternate hypotheses.
(b) Compute the -value.
(c) At the a=0.01, can you conclude that greater than 69% of emails are spam?
(d) At the a=0.05, can you conclude that greater than 69% of emails are spam?
Answer and step-by-step explanation:
a)
The required hypothesis are
H₀: [tex]\mu[/tex] = 0.69
H₁: [tex]\mu[/tex] > 0.69
additional solutions are attached in the image below
Answer:
a) No
B) Yes
Step-by-step explanation:
Calculating the p-value, we have;
z = (p-bar) -p/√(p(1-p)/n)
But p-bar = 365/500
= 0.73
Therefore,
z = 0.73 -0.69/√0.69(1-0.69)/500
= 0.04/√0.2139/500
= 0.04/√0.0004278
= 0.04/0.02068
= 1.93
p-value = p(z ≥1.93) = 0.0268
(a) Can you conclude that the percentage of emails that are spam is greater than 69% ?
No, because the p- value is greater than α. That is p-value⊃ 0.01
(b) Can you conclude that the percentage of emails that are spam is greater than 69%
Yes, since p-value ∠ 0.05
Joey read in his biology book that fish activity increases with water temperature, and he decided to investigate this issue by conducting an experiment. On nine successive days, he measured fish activity and water temperature in his aquarium. He found the equation of the LSRL to be y t ˆ = + 152.1 37.65 , where yˆ is the predicted amount of activity. If one of Joey’s days had a water temperature of 69.0 degrees Fahrenheit and the fish activity on that day was 265, what is the residual activity for this particular temperature?
The residual value is the difference between the actual and predicted values. Hence, the residual activity at a temperature of 69°F will be −2484.95
The equation of the Least Square Regression Line is given as :
y = 152.1 + 37.65tThe predicted amount of activity, y at a temperature of 69°F will be :
y = 152.1 + 37.65(69)
y = 2749.95
The actual amount of activity at a temperature of 69°F is 265
The residual activity at 69°F temperature can be calculated thus :
Residual = Actual - Predicted
Residual = 265 - 2749.95 = −2484.95
Therefore, the residual activity at 69°F is −2484.95
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TIME REMAINING
58:25
Roy wants to make a path from one corner of his yard to the other as shown below. The path will be 4 feet wide. He wants to
find the area of lawn that remains.
40 ft
15 ft
Roy claims that the area of the lawn is 300 square feet since it covers exactly one-half of the yard. Which statement about his
claim is correct?
He is incorrect. The path will have an area of (4)(40) = 160 sq ft. The yard has an area of 600 sq ft. The area of the lawn
will be the difference of the yard and path, so it is 440 sq ft.
Mark this and return
Save and Exit
Next
Submit
Answer:
YOUR CORRECT ANSWER IS(B.)Step-by-step explanation:
In ΔBCD, the measure of ∠D=90°, CB = 25, BD = 7, and DC = 24. What is the value of the sine of ∠C to the nearest hundredth?
Answer: The value of the sine of ∠C is 0.28.
Step-by-step explanation:
Let's draw a triangle again (see the picture below).
Remember SOHCAHTOA? It's:
-sin = opposite/hypotenuse
-cos = adjacent/hypotenuse
-tan = opposite/adjacent.
We need to use sin in here.
The sin of C is [tex]\frac{7}{25}[/tex], which in a calculator, gives [tex]0.28[/tex]
Recipes for the same type of cookies can vary in terms of ingredients and baking times. From a collection of chocolate chip cookie recipes, a baker randomly selected 5 recipes. From a collection of oatmeal raisin cookie recipes, the baker randomly selected 4 recipes. The mean baking times, in minutes, for each sample were recorded as x¯C and x¯O, respectively. What is the correct unit of measure for the standard deviation of the sampling distribution of x¯C−x¯O?
Answer:
answer should be minutes.
Step-by-step explanation:
in the problem, it is stated that the mean is in "baking times." this can lead one to assume that the standard deviation between the two xC-xO can be the variation in minutes that the two cookies types have.
A movie production company is releasing a movie with the hopes of many viewers returning to see the movie in theater for a 2nd time. The target is to have 30 million viewers and they want more than 30% of the viewers to return to see the movie again. They show the movie to a test audience of 200 people. After the movie they asked them if they would see the movie in theaters again. Of the test audience 68 people said they would see it again.
A. Explain what the p-value is
B. What is the p-value for the test statistic.
C. What is the statistical devision when the alpha=0.05
D. Explain the managerial conclusion for this situation.
Answer: p-value = 0.1085 and we will not reject the null hypothesis.
Step-by-step explanation:
Since we have given that
Hypothesis are :
[tex]H_0:p=0.3\\\\H_1:p>0.3[/tex]
Here, n = 200
x = 68
So, [tex]\hat{p}=\dfrac{68}{200}=0.34[/tex]
So, the test statistic value would be :
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.34-0.3}{\sqrt{\dfrac{0.3\times 0.7}{200}}}\\\\z=\dfrac{0.04}{0.0324}\\\\z=1.234[/tex]
So, the value of statistic value is 1.234.
And the p-value = 0.1085 at 5% level of significance.
So, 0.1085 < 1.234,
So, we will not reject the null hypothesis.
Hence, p-value = 0.1085 and we will not reject the null hypothesis.
The p-value is a measure of the evidence against the null hypothesis in a hypothesis test. To calculate the p-value, we compare the observed proportion to the target percentage using a one-sample proportion test. The statistical decision when alpha = 0.05 is to reject the null hypothesis if the p-value is less than 0.05.
Explanation:A. The p-value is a measure of the evidence against the null hypothesis in a hypothesis test. It represents the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.
B. To calculate the p-value for the test statistic in this case, we need to perform a hypothesis test. We compare the proportion of viewers who would see the movie again (68/200 = 34%) to the target percentage of 30% using a one-sample proportion test.
C. The statistical decision when alpha = 0.05 is to reject the null hypothesis if the p-value is less than 0.05. This indicates strong evidence against the null hypothesis.
D. The managerial conclusion for this situation would depend on the p-value obtained. If the p-value is less than 0.05, we can conclude that there is strong evidence to suggest that more than 30% of the viewers would see the movie again. Otherwise, we cannot make a definitive conclusion.
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what is the value for x 3x - 2 = 16
Answer:
18
Step-by-step explanation:
I meant 6x3=18 -2=16 sorry for confusion
To find the value of x, you need to isolate/get the variable "x" by itself in the equation:
3x - 2 = 16 Add 2 on both sides
3x - 2 + 2 = 16 + 2
3x = 18 Divide 3 on both sides to get "x" by itself
[tex]\frac{3x}{3} =\frac{18}{3}[/tex]
x = 6
PROOF
3x - 2 = 16 Substitute/plug in 6 into "x" since x = 6
3(6) - 2 = 16
18 - 2 = 16
16 = 16
i need helppp please :(
Step-by-step explanation:
2 ( 8 - 3c) = 4c - 34
16 - 6c = 4c - 34
6c + 4c = 16 + 34
10c = 50
c = 50/ 10
therefore c = 5
Hope it will help :)
Private universities claim to offer a higher quality education compared to public universities as justification for their more expensive tuition rates. The implication is that better education in the classroom leads to better employees after graduation. As a HR specialist in charge of selecting the best possible future employees from a pool of applicants, you propose giving preference to applicants with degrees from private universities. Hoping to control for the influence of academic performance on on-the-job performance, you randomly select 25 pairs of employees based on their cumulative GPA, one with a degree from a private university and another with a degree from a public university, and record their last performance evaluation score in an Excel file. The data appears as follows:
GPA Private University Alumni Public University Alumni
4.0 85 89
3.9 82 78
3.8 75 77
3.7 91 72
(a) How should this study design be described?
O True experiment
O Posttest only quasi experiment
O Non-experimental study
O Quasi experiment
Answer:quasi experiment
Step-by-step explanation:
Because it is basically for comparison usually by measuring outcomes if a program by participants and non participants
In a population of 210 women, the heights of the women are normally distributed with a mean of 64.4 inches and a standard deviation of 2.9 inches. If 36 women are selected at random, find the mean mu Subscript x overbar and standard deviation sigma Subscript x overbar of the population of sample means. Assume that the sampling is done without replacement and use a finite population correction factor. Round to two decimal places.
Given Information:
Population size = N = 210
Mean height of women population = μ = 64.4 in.
Standard deviation of height of women population = σ = 2.9 in.
Sample size = n = 36
Required Information:
Sample mean = μx = ?
Sample standard deviation = σx = ?
Answer:
Sample mean = μx = 64.4 in.
Sample standard deviation = σx = 0.44 in.
Step-by-step explanation:
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
The mean of the sample will be same as population mean that is
μ = μx = 64.4 in
Whereas the sample standard deviation is given by
[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \cdot \sqrt{\frac{N-n}{N-1} }[/tex]
Where σ is the standard deviation of height of women population, N is the population size and n is the sample size.
The term [tex]\sqrt{\frac{N-n}{N-1} }[/tex] is known as finite population correction factor and is used since the sampling is done without replacement.
[tex]\sigma_{x} = \frac{2.9}{\sqrt{36} } \cdot \sqrt{\frac{210-36}{210-1} }\\\sigma_{x} = 0.483 \cdot \sqrt{\frac{174}{209} }\\\sigma_{x} = 0.483 \cdot 0.912\\\sigma_{x} = 0.44[/tex]
Therefore, the standard deviation of sample is 0.44 in.
To find the mean (mu Subscript x overbar) and standard deviation (sigma Subscript x overbar) of the population of sample means, use the formulas provided.
Explanation:To find the mean (mu Subscript x overbar) and standard deviation (sigma Subscript x overbar) of the population of sample means, we use the formulas:
Mean of sample means (mu Subscript x overbar) = population mean (mu)Standard deviation of sample means (sigma Subscript x overbar) = population standard deviation (sigma) divided by the square root of the sample size (n), multiplied by the finite population correction factor (sqrt(N-n)/sqrt(N-1))In this case, the population mean (mu) = 64.4 inches, the population standard deviation (sigma) = 2.9 inches, and the sample size (n) = 36.
Using these values, we can calculate:
Mean of sample means (mu Subscript x overbar) = 64.4 inchesStandard deviation of sample means (sigma Subscript x overbar) = (2.9 inches) / sqrt(36) * sqrt(210-36) / sqrt(210-1) = 0.483 inchesLearn more about Population here:https://brainly.com/question/15889243
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Davis performed an experiment in which he spun a 4-color spinner 20 times. He recorded his results in the frequency table.
Davis predicts that if he spins the spinner another 20 times, the frequency for the red and green segments will still be equal. Is Davis correct?
Yes. Another experiment will give the same numbers as the first experiment.
Yes. The experimental probabilities remain the same for all experiments.
No. The frequencies will be multiplied by 20.
No. The frequencies and probabilities for red and green segments might change in the next experiment.
Answer:
No. The frequencies and probabilities for red and green segments might change in the next experiment.
Step-by-step explanation:
I just did it and it said my answer was right
Answer:
Step-by-step explanation:
No. The frequencies and probabilities for red and green segments might change in the next experiment.
i just did it and got it right so i hope you do too
A national magazine took a poll to determine company's opinions about outsourcing. Outsourcing is defined as the assignment of critical, but non-core, business functions to outside specialists. The magazine found that 26 percent of business executives felt that the benefits of outsourcing were less than what they expected. A sample of 100 business executives was polled. In this sample 19% of the business executives felt the benefits of outsourcing were less than what they expected. You want to determine whether the proportion of business executives in the sample differs from the national magazine poll. Which statistical test should you use?
Answer:
Hypothesis test on a proportion.
There is no enough evidence to support the claim that the proportion of business executives in the sample differs from the national magazine poll.
Step-by-step explanation:
We should test the hypothesis of the proportion, with a z-statistic.
The claim is that the proportion of business executives in the sample differs from the national magazine poll.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.26\\\\H_a:\pi<0.26[/tex]
The significance level is assumed to be 0.05.
The sample, of size n=100, has a proportion p=0.19.
The standard error for the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.26*0.74}{100}}=\sqrt{0.001924}=0.044[/tex]
Then, the z-statistic can be calculated as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.19-0.26+0.5/100}{0.044}=\dfrac{-0.065}{0.044}=-1.477[/tex]
The P-value for this one-tailed test is:
[tex]P-value=P(z<-1.477)=0.07[/tex]
As the P-value is bigger than the significance level, the effect is not significant. The null hypothesis failed to be rejected.
There is no enough evidence to support the claim that the proportion of business executives in the sample differs from the national magazine poll.
Somebody please help me with this i have no clue how to do any of this
Ms. Vargas recorded the hourly wage of each employee at her business.
Which of the following statements are true?
Chose all correct answers.
A. The mean of the data describes how the hourly wages vary.
B. The mean absolute deviation of the data describes how the hourly wages vary. C. The interquartile range of the data summarizes the hourly wages.
D. The median of the data summarizes the hourly wages.
E.The maximum value of the data summarizes the hourly wages.
Answer:
I think it is A and B. Not one hundred percent sure but,50 percent sure.
Step-by-step explanation:
Answer:
B.) and D.)
Step-by-step explanation:
Find the Jacobian ∂(x, y, z) ∂(u, v, w) for the indicated change of variables. If x = f(u, v, w), y = g(u, v, w), and z = h(u, v, w), then the Jacobian of x, y, and z with respect to u, v, and w is ∂(x, y, z) ∂(u, v, w) = ∂x ∂u ∂x ∂v ∂x ∂w ∂y ∂u ∂y ∂v ∂y ∂w ∂z ∂u ∂z ∂v ∂z ∂w . x = 1 6 (u + v), y = 1 6 (u − v), z = 6uvw
Answer:
The Jacobian ∂(x, y, z) ∂(u, v, w) for the indicated change of variables
= -3072uv
Step-by-step explanation:
Step :-(i)
Given x = 1 6 (u + v) …(i)
Differentiating equation (i) partially with respective to 'u'
[tex]\frac{∂x}{∂u} = 16(1)+16(0)=16[/tex]
Differentiating equation (i) partially with respective to 'v'
[tex]\frac{∂x}{∂v} = 16(0)+16(1)=16[/tex]
Differentiating equation (i) partially with respective to 'w'
[tex]\frac{∂x}{∂w} = 0[/tex]
Given y = 1 6 (u − v) …(ii)
Differentiating equation (ii) partially with respective to 'u'
[tex]\frac{∂y}{∂u} = 16(1) - 16(0)=16[/tex]
Differentiating equation (ii) partially with respective to 'v'
[tex]\frac{∂y}{∂v} = 16(0) - 16(1)= - 16[/tex]
Differentiating equation (ii) partially with respective to 'w'
[tex]\frac{∂y}{∂w} = 0[/tex]
Given z = 6uvw ..(iii)
Differentiating equation (iii) partially with respective to 'u'
[tex]\frac{∂z}{∂u} = 6vw[/tex]
Differentiating equation (iii) partially with respective to 'v'
[tex]\frac{∂z}{∂v} =6 u (1)w=6uw[/tex]
Differentiating equation (iii) partially with respective to 'w'
[tex]\frac{∂z}{∂w} =6 uv(1)=6uv[/tex]
Step :-(ii)
The Jacobian ∂(x, y, z)/ ∂(u, v, w) =
[tex]\left|\begin{array}{ccc}16&16&0\\16&-16&0\\6vw&6uw&6uv\end{array}\right|[/tex]
Determinant 16(-16×6uv-0)-16(16×6uv)+0(0) = - 1536uv-1536uv
= -3072uv
Final answer:-
The Jacobian ∂(x, y, z)/ ∂(u, v, w) = -3072uv
The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 900 voters in the town and found that 75% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is above 72%. Determine the P-value of the test statistic. Round your answer to four decimal places.
Answer:
P-value of the test statistic: P=0.0266.
Step-by-step explanation:
Hypothesis test on a proportion.
The claim is that the percentage of residents who favor annexation is above 72% This is going to be stated in the alternative hypothesis.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.72\\\\H_a:\pi>0.72[/tex]
The sample size is n=900 and the sample proportion is p=0.75.
The standard devaition is calculated as:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.72*0.28}{900}}=\sqrt{0.000224}=0.015[/tex]
Then, the z-statistic is:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.75-0.72-0.5/900}{0.015}=\dfrac{0.029}{0.015} = 1.9333[/tex]
For this right tailed test, the P-value is:
[tex]P-value=P(z>0.1933)=0.0266[/tex]
What property is 1/5+1/8=1/8+1/5?
Answer: This is the Communitve Property because the equation has the same thing on both sides, but the numbers "flip flopped" or switched around.
What is the measure of angle DEG on circle O? Please help! 50 points!
Answer:
50 degrees
Step-by-step explanation:
Which events have a probability of 25 percent? Select three options.
Answer:
The answer is A, C, E
A: choosing a green jelly bean out of a bag that contains 2 green jelly beans, 1 red jelly bean, and 5 yellow jelly beans
C: spinning a number less than 2 on a spinner that has four equal sections numbered from 1 to 4
D: choosing a spade out of a standard deck of cards that contains 13 hearts, 13 clubs, 13 diamonds, and 13 spades
Therefore the answer is A,C,E
Edg : )