MATH-225N Week 6 Assignment: Estimating Sample Size for a Population Proportion
1. Suppose an automotive repair company wants to determine the current
... [Show More] percentage of customers who keep up with regular vehicle maintenance. How many customers should the company survey in order to be 90% confident that the estimated (sample) proportion is within 2 percentage points of the true population proportion of customers who keep up with regular vehicle maintenance?
423
2. Suppose a shoe store wants to determine the current percentage of customers who are males. How many customers should the company survey in order to be 90% confident that the estimated (sample) proportion is within 3 percentage points of the true population proportion of customers who are males?
752
3. Deborah wants to estimate the percentage of people who eat fast food at least once per week. She wants to create a 90% confidence interval which has an error bound of at most 3%. How many people should be polled to create the confidence interval?
752
4. Suppose an automotive repair company wants to determine the current percentage of customers who keep up with regular vehicle maintenance. How many customers should the company survey in order to be 95% confident that the estimated (sample) proportion is within 5 percentage points of the true population proportion of customers who keep up with regular vehicle maintenance?
385
5. Question
Suppose a clothing store wants to determine the current percentage of customers who are over the age of forty. How many customers should the company survey in order to be 92% confident that the estimated (sample) proportion is within 3 percentage points of the true population proportion of customers who are over the age of forty? 852
6. Suppose an automotive repair company wants to determine the current percentage of customers who keep up with regular vehicle maintenance. How many customers should the company survey in order to be 90% confident that the estimated (sample) proportion is within 5 percentage points of the true population proportion of customers who keep up with regular vehicle maintenance? 271
7. Suppose a shoe store wants to determine the current percentage of customers who are males. How many customers should the company survey in order to be 98% confident that the estimated (sample) proportion is within 3 percentage points of the true population proportion of customers who are males? 1,503
8. Virginia wants to estimate the percentage of students who live more than three miles from the school. She wants to create a 95% confidence interval which has an error bound of at most 5%. How many students should be polled to create the confidence interval? 385
9. Suppose an automotive repair company wants to determine the current percentage of customers who keep up with regular vehicle maintenance. How many customers should the company survey in order to be 95% confident that the estimated (sample) proportion is within 2 percentage points of the true population proportion of customers who keep up with regular vehicle maintenance? 2,401
10. Emma wants to estimate the percentage of people who use public transportation. She surveys 140 individuals and finds that 100 use public transportation. What is the sample proportion for successes, p′? 0.714
11. Emma wants to estimate the percentage of people who use public transportation. She surveys 140 individuals and finds that 100 use public transportation. What are the sample proportion for failures, q′?
=0.286
12. Using the information from above, with p′=0.714, q′=0.286, and n=140, what is the 90% confidence interval for the proportion of the population who use public transportation? 0.651 and 0.777.
13. The Pew Social Media Update 2014 surveyed 1,597 adult internet users on which social media websites they use. Of the users surveyed, 1,134 responded "yes" when asked if they use Facebook. What is the value of p′, the estimate proportion of Facebook users in this research study?
p′=xn=1134/1597=0.71
14. The Pew Social Media Update 2014 surveyed 1,597 adult internet users on which social media websites they use. Of the users surveyed, 1,134 responded "yes" when asked if they use Facebook. From the question above, we know that p′=0.71. What is the error bound for proportions (EBP) of a confidence interval with a 99% confidence level? 0.029.
15. The Pew Social Media Update 2014 surveyed 1,597 adult internet users on which social media websites they use. Of the users surveyed, 1,134 responded "yes" when asked if they use Facebook. What is the confidence interval, at the 99% confidence level, for the proportion of the population of internet users that use facebook? (0.681,0.739)
16. Daniel wants to estimate the percentage of people who play sports. He surveys 360 individuals and finds that 75 play sports. What is the sample proportion for successes, p′?
p′=xn=75/360=0.208
16. Daniel wants to estimate the percentage of people who play sports. He surveys 360 individuals and finds that 75 play sports. What is the sample proportion for failures, q′?
Since p′+q′=1, we can solve for q′.
q′=1−p′=1−0.208=0.792
17. Using the information from above, with p′=0.208, q′=0.792, and n=360, what is the 95% confidence interval for the proportion of the population who play sports?
We know n=360 , p′=0.208 , and q′=0.792 . Since the confidence level is 95% , α=1−0.95=0.05 , and α2=0.025 . The z -value for z0.025 is 1.96 .
EBP=(zα2)(p′q′n−−−−√)=(1.96)((0.208)(0.792)360−−−−−−−−−−−−√)≈(1.960)(0.000458−−−−−−−√)≈0.042
So we can write the confidence interval as (0.208−0.042,0.208+0.042)=(0.166,0.250) . We estimate with 95% confidence that the true population proportion of people who play sports is between 0.166 and 0.250 .
18. The population mean of a set of data is unknown. The sample mean is 29, and the error bound for the mean is 4, at a 68% confidence level. (So, x¯=29 and EBM = 4.) Find and interpret the confidence interval estimate.
-We can estimate, with 68% confidence that the true value of the population mean is between 25 and 33.
19. Suppose a shoe store wants to determine the current percentage of customers who are males. How many customers should the company survey in order to be 92% confident that the estimated (sample) proportion is within 4 percentage points of the true population proportion of customers who are males? 480
20. Billy wants to estimate the percentage of students who live more than three miles from the school. He wants to create a 95% confidence interval which has an error bound of at most 3%. How many students should be polled to create the confidence interval? 1,068
21. Suppose an internet marketing company wants to determine the current percentage of customers who click on ads on their smartphones. How many customers should the company survey in order to be 98% confident that the estimated proportion is within 5 percentage points of the true population proportion of customers who click on ads on their smartphones? 542
22. Jason wants to estimate the percentage of people who sleep for at least seven hours each night. He wants to create a 92% confidence interval which has an error bound of at most 3%. How many people should be polled to create the confidence interval? 852
23. Suppose a clothing store wants to determine the current percentage of customers who are over the age of forty. How many customers should the company survey in order to be 98% confident that the estimated (sample) proportion is within 2 percentage points of the true population proportion of customers who are over the age of forty? 3,382
24. Ariana wants to estimate the percentage of people who play a musical instrument. She surveys 380 individuals and finds that 260 play a musical instrument. What is the sample proportion for successes, p′? 0.684
25. Ariana wants to estimate the percentage of people who play a musical instrument. She surveys 380 individuals and finds that 260 play a musical instrument. What is the sample proportion for failures, q′? =0.316
26. Using the information from above, with p′=0.684, q′=0.316, and n=380, what is the 90% confidence interval for the proportion of the population who play a musical instrument? 0.645 and 0.723.
27. Suppose a pizza company wants to determine the current percentage of customers who eat pizza more than twice a month. How many customers should the company survey in order to be 98% confident that the estimated (sample) proportion is within 4 percentage points of the true population proportion of customers who eat pizza more than twice a month?
846
28. Brenda wants to estimate the percentage of people who eat fast food at least once per week. She wants to create a 95% confidence interval which has an error bound of at most 2%. How many people should be polled to create the confidence interval? 2401
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