According to the hypothesis sample size and test statistic i

According to the hypothesis, sample size, and test statistic, i) find the reject region, ii) critical value, then iii) estimate p value from the t-table, finally iv) state the conclusion for the following case, when alpha = 0.05

a) Ho: mu = 5, Ha: mu > 5 , Sample size is 17, ts= 1.4

b)Ho: mu = 5, Ha: mu < 5, Sample size is 10 , ts= -0.5

Solution

a) Ho: mu = 5, Ha: mu > 5 , Sample size is 17, ts= 1.4

i) find the reject region,

The degree of freedom =n-1=17-1=16

Given a=0.05, the critical value is t(0.05, df=16) =1.746 (from student t table)

So the reject region is if t>1.746, we reject HO

ii) critical value, then

Given a=0.05, the critical value is t(0.05, df=16) =1.746 (from student t table)

iii) estimate p value from the t-table, finally

the p-value= P(t with df=16 >1.4) =0.0903 (from student t table)

iv) state the conclusion for the following case, when alpha = 0.05

Since the p-value is greater than 0.05, we do not reject Ho.

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b)Ho: mu = 5, Ha: mu < 5, Sample size is 10 , ts= -0.5

i) find the reject region,

The rejection region is if t<-1.833, we reject Ho.

ii) critical value, then

The degree of freedom =10-1=9

Given a=0.05, the critical value is t(0.05, df=9) =-1.833

iii) estimate p value from the t-table, finally

The p-value= P(t with df=9 <-0.5) =0.3145 (from student t table)

iv) state the conclusion for the following case, when alpha = 0.05

Since the p-value is larger than 0.05, we do not reject Ho.