210 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 57 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 four decimal places.) (c) Calculate a 90% confidence interval for the population proportion. (Round the answers to three decimal places.) to _ (d) Calculate a 95% confidence interval for the population proportion. (Round the answers to three decimal places.) to (e) Calculate a 98% confidence interval for the population proportion. (Round the answers 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 decreased, the width of the interval increases. As the confidence level is increased, the width of the interval decreases. As the confidence level is decreased, the width of the interval decreases. As the confidence level is increased, 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

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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210 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 57 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 four decimal places.)

(c) Calculate a 90% confidence interval for the population proportion. (Round the answers to three decimal places.)
__to ___

(d) Calculate a 95% confidence interval for the population proportion. (Round the answers to three decimal places.)
__to __

(e) Calculate a 98% confidence interval for the population proportion. (Round the answers 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 decreased, the width of the interval increases.

As the confidence level is increased, the width of the interval decreases.

As the confidence level is decreased, the width of the interval decreases.

As the confidence level is increased, 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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