170 students were asked to randomly pick one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The number 7 was picked by 53 students. (a) For the sample, calculate the proportion of students who picked 7. (Round the answer to three decimal places.) (b) Calculate the standard error for this sample proportion. (Round the answer to three decimal places.) (c) Calculate a 90% confidence interval for the population proportion. (Round the answer to three decimal places.) ___to___
170 students were asked to randomly pick one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The number 7 was picked by 53 students. (a) For the sample, calculate the proportion of students who picked 7. (Round the answer to three decimal places.) (b) Calculate the standard error for this sample proportion. (Round the answer to three decimal places.) (c) Calculate a 90% confidence interval for the population proportion. (Round the answer to three decimal places.) ___to___
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 30PPS
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Question
170 students were asked to randomly pick one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The number 7 was picked by 53 students.
(a) For the sample, calculate the proportion of students who picked 7. (Round the answer to three decimal places.)
(b) Calculate the standard error for this sample proportion. (Round the answer to three decimal places.)
(c) Calculate a 90% confidence interval for the population proportion. (Round the answer to three decimal places.)
___to___
(d) Calculate a 95% confidence interval for the population proportion. (Round the answer to three decimal places.)
___to___
(e) Calculate a 98% confidence interval for the population proportion. (Round the answer to three decimal places.)
__to__
(f) What do the results of parts (c)-(e) indicate about the effect of confidence level on the width of a confidence interval? (Select all that apply.)
(b) Calculate the standard error for this sample proportion. (Round the answer to three decimal places.)
(c) Calculate a 90% confidence interval for the population proportion. (Round the answer to three decimal places.)
___to___
(d) Calculate a 95% confidence interval for the population proportion. (Round the answer to three decimal places.)
___to___
(e) Calculate a 98% confidence interval for the population proportion. (Round the answer to three decimal places.)
__to__
(f) What do the results of parts (c)-(e) indicate about the effect of confidence level on the width of a confidence interval? (Select all that apply.)
As the confidence level is increased, the width of the interval decreases.
As the confidence level is increased, the width of the interval increases.
As the confidence level is decreased, the width of the interval decreases.
As the confidence level is decreased, the width of the interval increases.
(g) On the basis of these confidence intervals, do you think that students choose numbers "randomly"?
Yes or No
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