Question

Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 20% 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 "O". 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? the null hypothesis. We can conclude that the proportion of business reject 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 "O". Do not round your intermediate calculations. The smallest level of significance for which we could draw this conclusion is a=0.05, we reject 3; because p-value less than or equal to the null hypothesis.

Answer 1

Part a: So the number of business owners giving holiday gift to their employees from survey is 12.

Part b: p-value is 0.00003

Part c: value of p is less that a we reject the null hypothesis.

Explanation:

Part a

number of business owners=20% x n

number of business owners= 0.2x 60

number of business owners=12

Part b

H0: p=0.46

H1: p<0.46

Here

n=60,
`\hat{p}`=0.2, p=0.46

So test statistics is given as

`z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}\\z=\frac{0.20-0.46}{\sqrt{(0.46(1-0.46))/(60)}}\\z=(-0.26)/(0.064)\\z=-4.04`

p-value is P(z<-4.04)= 0.00003

Part c

As value of p is less that a we reject the null hypothesis.