Question

students at arkansas campus were measured for their liking of ethnic cuisines on a scale of 1 to 5. campus dining will start offering these cuisines if the score is 3.5 or greater. 100 randomly picked students filled out the survey. the mean was 3.6 with a sample standard deviation of 0.5 HINT:use t-ditribution for this question

a. what is the null hypothesis and the alternative hypothesis in English? use HO to label the null and H1 for alternate. b. what are the null and alternative hypotheses in statistical terms, using math symbols?

c. should campus dining offer ethnic cuisines, based on this survey? show your calculations on how you disproved or failed to disprove the null hypothesis

Answer 1

a)

Null hypothesis = Population mean score is equal to 3.5

Alternative hypothesis = Population mean score is greater than 3.5

b)

H0: = 3.5

Ha: > 3.5

c)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 3.6 - 3.5 ) / ( 0.5 / √(100) )
t = 2

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 100-1) = 1.66

t > t(α, n-1) = 2 > 1.66
Result :- Reject null hypothesis

We have sufficient evidence to support the claim that campus dining will start offering these cuisines.