Mimi is interested in testing the claim that banana is the favorite fruit for mo
ID: 3289563 • Letter: M
Question
Mimi is interested in testing the claim that banana is the favorite fruit for more than 50% of the adults. She conducted a survey on a random sample of 100 adults. 58 adults in the sample chose banana as his I her favorite fruit. Assume Mimi wants to use a 0.10 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 50% of the adults? Explain.
Explanation / Answer
(a) Nul Hypothesis : H0 : p = 0.50
Alternative Hypothesis : Ha : p > 0.50
(b) First we willl calculate standard error of the proportion se0 = sqrt [p(1-p)/ N] = sqrt [0.5 * 0.5/ 100] = 0.05
Test Statistic
Z = (p^ - 0.50)/ se0 = ( 0.58 - 0.50)/ 0.05
Z = 1.60
(c) P - value = Pr ( p > 0.58; 0.50 ; 0.05)
Z = 1.60
so p- value = Pr( Z> 1.6)
from Z - table
Pr( Z >1.6) = 1 - 0.9452 = 0.0548
(d) Here p - value (0.0548) < significance level alpha 0.10 so we will reject the null hypothesis and conclude that there is enough evidence to support the claim that banana is the favorite fruit for more than 50% of the adults.