Question

Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 40% 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? 24 (b) Suppose the business owners in the sample do 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. If required, round your answer to four decimal places. If your answer is zero, enter “0”. Do not round your intermediate calculations. (c) Using a 0.05 level of significance, would you conclude that the proportion of business owners providing gifts has decreased? Do we - reject or fail to reject the null hypothesis. We - Select your answer -can or cannot conclude that the proportion of business owners providing gifts has decreased from 2008 to 2009. What is the smallest level of significance for which you could draw such a conclusion? If required, round your answer to four decimal places. If your answer is zero, enter “0”. Do not round your intermediate calculations. The smallest level of significance for which we could draw this conclusion is ____________ ; because p-value - is less than or equal to or greater than α=0.05, we - Select your answer -reject or fail to reject the null hypothesis.

Answer 1

(a)

Number of business owners in the survey plan to provide holiday gift to their employees = 60 X 40/100 = 24

(b)

P = Population Proportion = 0.46

Q =1 - p = 0.54

n = Sample Size = 60

SE =

Test statistic is given by:
Z = (0.40 - 0.46)/0.0643 = - 0.9325

By technology,

P - value is 0.1755

(c)

Correct option:

We cannot conclude that that the proportion of business owners proving gifts has decreased from 2008 to 2009.

The smallest level of significance for which we could draw such a conclusion = 0

because p - value is greater than =0.05, we fail to reject the null hypothesis.

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