Question

Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 30% 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?
(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?
	We - Select your answer to the null hypothesis. We - Select your answer 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 - Select your answer - α=0.05, we - Select your answer the null hypothesis.

Answer 1

a)

30% of business owners in the survey size of 60 plan to provide a holiday gift to their employees

b)

To test whether there is significant difference in results from survey, the z test for the one proportion is used.

The null and alternative hypotheses are defined as,

The z-statistic is obtained using the formula,

The p-value is obtained from z-distribution table for z = -2.487

Since the P-value is 0.0064<0.05 at 5% significant level, the null hypothesis is rejected. Hence we can conclude that the proportion is decreased.

c)

Since the null hypothesis is rejected at 5% significance level, we can conclude that the proportion of business owners providing gifts has decreased.

The P-value for the hypothesis test is,

Based on the P-value, the smallest level of significance for which we could draw this conclusion is 0.7%