Question

suppose that a random sample of 16 measures from a normally distributed population gives a sample mean of x=13.5 and a sample standard deviation of s=6. the null hypothesis is equal to 15 and the alternative hypothesis is not equal to 15. using hypothesis testing for t values do you reject the null hypothesis at alpha=.10 level of significance?

Answer 1

Solution :

Given that,

Population mean = = 15

Sample mean = = 13.5

Sample standard deviation = s = 6

Sample size = n = 16

Level of significance = = 0.10

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 15

Ha: 15

The test statistics,

t = ( - )/ (s/)

= ( 13.5 - 15 ) / ( 6 /16)

= -1

p-value = 0.3332 ( using t- distribution probability table)

The p-value is p = 0.3332 > 0.10, it is concluded that the null hypothesis is fail to reject.

Conclusion:

It is concluded that the null hypothesis Ho is fail to reject. Therefore, there is not enough evidence to claim that the population

mean μ is different than 15, at the 0.10 significance level.