Answer each of the following questions. Point values are indicated with each que
ID: 3314231 • Letter: A
Question
Answer each of the following questions. Point values are indicated with each question.
Please could you go over my answers to see if I am in the ballpark or I need to make adjustments? thank you.
(20 pts.) State your question. Remember that your question should be related to the population proportion or proportions and should be one that will require the use of a confidence interval and hypothesis test to answer. Assume that your sample is representative of the population.
Is the proportion of juniors less than 20% of the student body?
(30 pts.) Explain the methodology you will use to answer the question you posed. Your explanation should include answers to the following questions. Do not include your analysis or answers to your question here—only describe how you will do the analysis.
What is the variable of interest?
The variable of interest is the student body and the number of juniors in the class.
What confidence interval will you use?
I will use a 95% confidence interval for the population proportion.
What are your null and alternate hypotheses?
Is it a one-sample or two-sample test?
This is a one sample test of the population proportion.
Is it an upper (right)-, lower (left)-, or two-tail test?
Because the sign of the inequality is less than, this would be a lower (left)- tailed test.
What level of significance will you use and why?
Because the data level wasn’t given the preferred level is 0.05 which coincides with a 95% confidence interval.
Are the conditions necessary for a confidence interval and hypothesis test for the population proportion satisfied? Explain.
My sample size is 30, there are 9 juniors so the proportion of juniors in the class is 9/30 = .3.
The conditions are shown on page 324 and 338 using the second edition vice the first.
Random Sample: The sample was randomly selected from the population of StatCrunchU students.
For the confidence interval, there should be at least 10 successes and 10 failures in the sample. In the case there is 9 juniors (successes) and 21 others (failures). For the hypothesis test there must be at least 10 expected successes and 10 expected failures in the sample if the null hypothesis is true.However, in this case NOT ALL conditions are met because n*p0 = 30*0.20 = 6 and n*(1-p0) = 30*(1-.20) = 24.
Because sampling was done without replacement, the population must be at least 10 times larger than the sample. This is satisfied because the sample size is approximately 46,000 and the sample size is 30.
Items in the sample were independently selected.
(30 pts.) Carry out the methodology described in 2 above. Use StatCrunch and paste copies of the StatCrunch output in the space below. (NOTE: For the purposes of this assignment, go ahead and complete the confidence interval and hypothesis test even if there are not at least 10 successes and 10 failures.) Your explanation should include answers to the following questions:
What are the upper and lower bounds of the confidence interval?
One sample proportion summary confidence interval:
p : Proportion of successes
Method: Standard-Wald
95% confidence interval results:
Proportion
Count
Total
Sample Prop.
Std. Err.
L. Limit
U. Limit
p
9
30
0.3
0.083666003
0.13601765
0.46398235
What is the error term in the confidence interval?
The error term in the confidence interval is (.4640-.1360)/2= .164.
What does the confidence interval mean in terms of the question you posed?
I am 95% confident that the population proportion of juniors in StatCrunchU is between .1360 and .4640.
What is the p-value in your hypothesis test and what does it mean in terms of the question you posed?
One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.2
HA : p < 0.2
Hypothesis test results:
Proportion
Count
Total
Sample Prop.
Std. Err.
Z-Stat
P-value
p
9
30
0.3
0.073029674
1.3693064
0.9145
The p-value is .9145. That means if the null hypothesis that the proportion of juniors in the population is .20 is true, then the probability of getting a sample proportion of juniors of .3 or more in a sample size of 30 is .9145.
Did you reject or not reject the null hypothesis and why?
The null hypothesis would not be rejected because the p-value of .9145 is greater than the level of significance of 0.05.
What is the conclusion of your hypothesis test in terms of the question you posed?
There is no evidence that the proportion of juniors in StatCrunchU is lesser than .20.
Do the results of the confidence interval and hypothesis test agree? Explain.
The 95% confidence interval is between .1360 and .4640 and we did not reject the null hypothesis that the proportion of juniors equals .20 at the level of significance. The two agree because .20 is in the 95% confidence interval.
4. (20 pts.) Based on the results of 2 and 3 above, answer your question. Include an explanation of how you used the StatCrunch output to formulate your answer.
The question posted was Is the proportion of juniors less than 20% of the student body?
The 95% confidence interval contained .20 and the null hypothesis was not rejected. Therefore there is not enough evidence that the proportion of juniors in StatCrunchU is less than .20.
Proportion
Count
Total
Sample Prop.
Std. Err.
L. Limit
U. Limit
p
9
30
0.3
0.083666003
0.13601765
0.46398235
Explanation / Answer
20 pts.) State your question. Remember that your question should be related to the population proportion or proportions and should be one that will require the use of a confidence interval and hypothesis test to answer. Assume that your sample is representative of the population.
Is the proportion of juniors less than 20% of the student body?
Correct
(30 pts.) Explain the methodology you will use to answer the question you posed. Your explanation should include answers to the following questions. Do not include your analysis or answers to your question here—only describe how you will do the analysis.
What is the variable of interest?
The variable of interest is the student body and the number of juniors in the class.
Correct
What confidence interval will you use?
I will use a 95% confidence interval for the population proportion.
Correct
What are your null and alternate hypotheses?
Null : proportion of juniors is not less than 20% of the student body
Alternate : proportion of juniors is less than 20% of the student body
Is it a one-sample or two-sample test?
This is a one sample test of the population proportion.
Yes , as we are interested in the “less than “ claim of the test
Is it an upper (right)-, lower (left)-, or two-tail test?
Because the sign of the inequality is less than, this would be a lower (left)- tailed test.
Correct
What level of significance will you use and why?
Because the data level wasn’t given the preferred level is 0.05 which coincides with a 95% confidence interval.
Are the conditions necessary for a confidence interval and hypothesis test for the population proportion satisfied? Explain.
My sample size is 30, there are 9 juniors so the proportion of juniors in the class is 9/30 = .3.
The conditions are shown on page 324 and 338 using the second edition vice the first.
Random Sample: The sample was randomly selected from the population of StatCrunchU students.
For the confidence interval, there should be at least 10 successes and 10 failures in the sample. In the case there is 9 juniors (successes) and 21 others (failures). For the hypothesis test there must be at least 10 expected successes and 10 expected failures in the sample if the null hypothesis is true.However, in this case NOT ALL conditions are met because n*p0 = 30*0.20 = 6 and n*(1-p0) = 30*(1-.20) = 24.
Because sampling was done without replacement, the population must be at least 10 times larger than the sample. This is satisfied because the sample size is approximately 46,000 and the sample size is 30.
Items in the sample were independently selected.
Correct , well defined
(30 pts.) Carry out the methodology described in 2 above. Use StatCrunch and paste copies of the StatCrunch output in the space below. (NOTE: For the purposes of this assignment, go ahead and complete the confidence interval and hypothesis test even if there are not at least 10 successes and 10 failures.) Your explanation should include answers to the following questions:
What are the upper and lower bounds of the confidence interval?
One sample proportion summary confidence interval:
p : Proportion of successes
Method: Standard-Wald
95% confidence interval results:
Proportion
Count
Total
Sample Prop.
Std. Err.
L. Limit
U. Limit
p
9
30
0.3
0.083666003
0.13601765
0.46398235
What is the error term in the confidence interval?
The error term in the confidence interval is (.4640-.1360)/2= .164.
What does the confidence interval mean in terms of the question you posed?
I am 95% confident that the population proportion of juniors is between .1360 and .4640.
What is the p-value in your hypothesis test and what does it mean in terms of the question you posed?
One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.2
HA : p < 0.2
Hypothesis test results:
Proportion
Count
Total
Sample Prop.
Std. Err.
Z-Stat
P-value
p
9
30
0.3
0.073029674
1.3693064
0.9145
The p-value is .9145. That means if the null hypothesis that the proportion of juniors in the population is .20 is true, then the probability of getting a sample proportion of juniors of .3 or more in a sample size of 30 is .9145.
Correct
Did you reject or not reject the null hypothesis and why?
The null hypothesis would not be rejected because the p-value of .9145 is greater than the level of significance of 0.05.
Correct
What is the conclusion of your hypothesis test in terms of the question you posed?
There is no evidence that the proportion of juniors in StatCrunchU is lesser than .20.
Do the results of the confidence interval and hypothesis test agree? Explain.
The 95% confidence interval is between .1360 and .4640 and we did not reject the null hypothesis that the proportion of juniors equals .20 at the level of significance. The two agree because .20 is in the 95% confidence interval.
Correct
4. (20 pts.) Based on the results of 2 and 3 above, answer your question. Include an explanation of how you used the StatCrunch output to formulate your answer.
The question posted was Is the proportion of juniors less than 20% of the student body?
The 95% confidence interval contained .20 and the null hypothesis was not rejected. Therefore there is not enough evidence that the proportion of juniors in StatCrunchU is less than .20.
The answers are well written .
Proportion
Count
Total
Sample Prop.
Std. Err.
L. Limit
U. Limit
p
9
30
0.3
0.083666003
0.13601765
0.46398235
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