Question

The null and alternate hypotheses are: H0 : μ1 = μ2 H1 : μ1 ≠ μ2 A random sample of 9 observations from one population revealed a sample mean of 22 and a sample standard deviation of 3.9. A random sample of 9 observations from another population revealed a sample mean of 27 and a sample standard deviation of 4.1. At the 0.01 significance level, is there a difference between the population means? State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) The decision rule is to reject HO if T< or t> . b) Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.) Pooled estimate of the population variance=? Compute the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Test Statistic=?

Answer 1

Given that,

Null and Alternative Hypotheses:-

[ Where Population mean for Adjuster 1 and Population mean for Adjuster 2 ]

Also given that,

Sample	Number of sample	Mean	SD
Sample 1	9	22	3.9
Sample 2	9	27	4.1

Now we want to test at the 0.01 significance level, is there a difference between the population means.

For this test our appropriate test statistic is given by,

[ Where,

Number of random sample for sample 1 = 9  ,   Number of random sample for sample 2 = 9

Sample Mean for sample 1 = 22 ,   Sample Mean for sample 2 = 27

Sample Standard Deviation for sample 1 = 3.9 ,       Sample Standard Deviation for sample 2 = 4.1

]

Decision rule:-

[ Value are getting from t-distribution probability table with corresponding , DF =16 and two tailed probability and round to three decimal places ]

Answer:- Since the test is two tailed test so, we reject the null hypothesis at level if we get,

or  

Pooled estimate of the population variance:-

Answer:- So we get, Pooled estimate of the population variance = 16.01

Value of the test statistic:- ( putting the value of , , , , )

[ Round to three decimal places ]

Answer:- Value of test statistic =

Decision:-

Here we get, , i.e. and

Result:- We do not reject the null hypothesis at level

Conclusion:- From the above testing result we can conclude that, at the 0.01 significance level there is not a significant difference between the two population means​​​​​​​.