Mimi is interested in testing the claim that banana is the favorite fruit for mo
ID: 3056700 • Letter: M
Question
Mimi is interested in testing the claim that banana is the favorite fruit for more than 80% of the adults. She conducted a survey on a random sample of 100 adults. 85 adults in the sample chose banana as his / her favorite fruit. Assume Mimi wants to use a 0.05 significance level to test the claim. (a) Identify the null hypothesis and the alternative hypothesis. (b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. (c) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit. (d) Is there sufficient evidence to support the claim that banana is the favorite fruit for more than 80% of the adults? Explain.
Explanation / Answer
H0: P = 0.8
H1: P > 0.8
The test statistic z = (p - P)/sqrt(P * (1 - P)/n)
= (0.85 - 0.8)/sqrt(0.8 * 0.2/100)
= 1.25
P-value = P(Z > 1.25)
= 1 - P(Z < 1.25)
= 1 - 0.8944
= 0.1056
As the p-value is greater than the significance level (0.1056 > 0.05), so the null hypothesis is not rejected.
So there is not sufficient evidence to support the claim that banana is the favourite fruit for more than 80% of the adults.