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.

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 ________?

Answer 1

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?

n=60, p=0.30

np=60*0.30 =18

(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.

One sample proportion test

Ho: P=0.46, H₁: P< 0.46

= -2.4867

P value = P( z < -2.4867)

= 0.0064

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.46
Level of Significance	0.05
Number of Items of Interest	18
Sample Size	60
Intermediate Calculations
Sample Proportion	0.3
Standard Error	0.0643
Z Test Statistic	-2.4867
Lower-Tail Test
Lower Critical Value	-1.645
p-Value	0.0064
Reject the null hypothesis

c.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 0.0064

(this corresponds to the p-value = 0.0064. p- value is also called the observed level of significance)