Question

A betting analyst in Las Vegas wants to study the losses suffered from gamblers at a particular casino to determine whether a particular casino is cheating. In particular, the analyst wants to see if gamblers' average losses exceed $45, which is the average from all other casinos. She selects a random sample of 60 gamblers and finds that the sample mean loss was $55 and the sample standard deviation was $40.

What are the critical values from the t distribution (with the relevant degrees of freedom) associated with a 95% confidence interval?

Answer 1

To Test :-  

H0 :-  

H1 :-  

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 55 - 45 ) / ( 40 / √(60) )
t = 1.9365

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
t(α, n-1) = t(0.05 , 60-1) = 1.671
t > t(α, n-1) = 1.9365 > 1.671
Result :- Reject null hypothesis

Critical value is t > t(α, n-1)   i.e   t > 1.671

There is sufficient evidence to support the claim that  gamblers' average losses exceed $45.