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.

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

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

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

   for obtaining the test statistic

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

   obtaining the p-value

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

6. (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

Null hypothesis  
H0: P =0.50          
              
Alternative hypothesis  
H1: P >0.50          
              
We have for given example,              
Population proportion value is =0.5          
x=56          
              
n=100          
Level of significance =   0.05          
Estimate for sample proportion = 0.56          
              
Z test statistic formula for proportion

      
P-value   0.1151          
Decision:   Do not reject   H0.      

Conclusion: We do not have sufficient evidence at level of significance 0.05 that,  banana is the favorite fruit for more than 50% of the adults.