A random sample of 10 has a mean of 110 Test the null hypoth

A random sample of 10 has a mean of 110. Test the null hypothesis that mu = 120 against the alternative hypothesis that mu

Solution

Sol:

Null Hypothesis;

Ho:=120

Alternative Hpothesis:

Ho:<120

level of significance=0.05

Test statistic:

sample size=n=10

sample mean=110

population standard deviation=18

`

t=110-120/18/sqrt(10)=-1.76

degrees of freedom=n-1=10-1=9

The P-Value is .056131.

The result is not significant at p < .05.

Fail to reject Null Hypothesis.

Accept null hypothesis.

There is insufficient evidence at 0.05 level of significance to support the claim that mean is less than 120 .

alpha=1-0.5=0.05

alpha/2=0.05/2=0.025

Solutionb:

sample sd=18

t=x-mean/sample sd/sqrt(n)

=110-120/18/sqrt(10)

=-1.76

degrees of freedom=n-1=10-1=9

The P-Value is .056131.

The result is not significant at p < .05.

Fail to reject Null Hypothesis.