Question

A grocery store manager is interested in testing the claim that banana is the favorite fruit for more than 50% of the adults. The manager conducted a survey on a random sample of 100 adults. The survey showed that 56 adults in the sample chose banana as his/her favorite fruit. Assume the manager wants to use a 0.05 significance level to test the claim.  

(a) What is the appropriate hypothesis test to use for this analysis? Please identify and explain why it is appropriate.

(b) Identify the null hypothesis and the alternative hypothesis.

(c) Determine the test statistic. Round your answer to two decimal places. Describe method used for obtaining the test statistic

(d) Determine the p-value. Round your answer to three decimal places. Describe method used for obtaining the p-value

(e) Compare p-value and significance level α. What decision should be made regarding the null hypothesis (e.g., reject or fail to reject) and why?

(f) Is there sufficient evidence to support the claim that banana is the favorite fruit for more than 50% of the adults? Explain your conclusion.

Answer 1

n = 100

x = 56

Claim: The banana is the favorite fruit for more than 50% of the adults.

a) we use one proportation z test because we are testing population proportion more than 50%

b)

Null and alternative hypothesis is

Level of significance = 0.05

c)

Test statistic is

d)

P-value = 0.115 ( Using z table)

p-value = p( z > 1.2) = 1-p(z<1.2)=1-0.8849=0.1151

also we use EXCEL command =NORMSDIST(z)

P-value = 0.115 ( Using z table)

e) Compare p-value and significance level α,we get result

P-value , Failed to Reject Ho

f) conclusion :  There is insufficient evidence to support the claim that banana is the favorite fruit for more than 50% of the adults