The following data come from a normal population having stan

The following data come from a normal population having standard deviation 4:

105

108

112

121

100

105

99

107

112

122

118

105

Use them to test the null hypothesis that the population mean is less than or equal to 100 at the

(a) 5 percent level of significance

(b) 1 percent level of significance

(c) What is the p value?

Solution

H0: mu = 100

Ha: mu <=100

First find out the sample mean

Sample mean =109.5

Mean difference = 9.5

Sample size = 12

Hence t test is used here

STd error = sigma/rt 12 = 4/rt 12

= 1.155

t statistic = 8.2272

p value = 0.9999

As p value > alpha at both 5% and 1% accept null hypothesis at both levels.

There is no statistical evidence to prove that sample mean <=100