Question

Last year, 57% 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?

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

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

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

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.)

Answer 1

a)

0.45 * 60 = 27 business owners

b)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.57
Alternative Hypothesis, Ha: p < 0.57

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.45 - 0.57)/sqrt(0.57*(1-0.57)/60)
z = -1.88

P-value Approach
P-value = 0.0302
As P-value < 0.05, reject the null hypothesis.

c)

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

0.0302 is the smallest level of significance