Last year, 60% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 45% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners. (a) How many business owners in the survey plan to provide a holiday gift to their employees this year? __ business owners. (b) Suppose the business owners in the sample did as they plan. Compute the p-value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year. Find the value of the test statistic. (Round your answer to two decimal places.) _. Find the p-value. (Round your answer to four decimal places.) p-value = . (c) Using a 0.05 level of significance, would you conclude that the proportion of business owners providing gifts decreased? Pick a letter a. Do not reject H0. There is insufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year. b. Reject H0. There is sufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year. C. Do not reject H0. There is sufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year. D. Reject H0. There is insufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year. What is the smallest level of significance for which you could draw such a conclusion? (Round your answer to four decimal places.) _______.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 13CYU

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Last year, 60% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 45% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners.

(a)

How many business owners in the survey plan to provide a holiday gift to their employees this year?

__________ business owners.

(b)

Suppose the business owners in the sample did as they plan. Compute the p-value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year.

Find the value of the test statistic. (Round your answer to two decimal places.)

_________________.

Find the p-value. (Round your answer to four decimal places.)

p-value = ______________.

(c)

Using a 0.05 level of significance, would you conclude that the proportion of business owners providing gifts decreased? Pick a letter

a. Do not reject H₀. There is insufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year.

b. Reject H₀. There is sufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year.

C. Do not reject H₀. There is sufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year.

D. Reject H₀. There is insufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year.

What is the smallest level of significance for which you could draw such a conclusion? (Round your answer to four decimal places.)

_____________.

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