Test Ho: µ =100; H1: µ < 100, using n = 36 and alpha = .05 If the sample mean=106 and the sample standard deviation = 15, which of the following is true?
A. test statistic = 2.4; the critical value = -1.69; we fail to reject Ho.
B. test statistic = 1.96; the critical value = -1.69; we fail to reject Ho.
C. test statistic = 2.40; the critical value = -1.69; we reject Ho.
D. test statistic = 2.40; the critical value = 1.69; we reject Ho
the correct option be:-
A. test statistic = 2.4; the critical value = -1.69; we fail to reject Ho.
[explanation:-
hypothesis:-
given data are:-
sample mean () = 106
sample sd (s)=15
sample size (n) =36
level of significance () = 0.05
here we will do 1 sample t test for mean.
test statistic be:-
degrees of freedom = (n-1)=(36-1)=35
t critical value for 95% confidence level = -1.69
[ using t distribution table for df = 35,alpha=0.05, left tailed test ]
rejection region:-
reject the null hypothesis if,
decision:-
so, we fail to reject the null hypothesis. ]
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