Question

Salary data from two random samples of high school teachers are shown to the right. Also shown are the population standard deviations.

Construct a 90% confidence interval to estimate the difference in the average salaries of the high school teachers in these two states.

b. Based on the results in part? a, can you conclude that a difference exists in the average? salaries?

	state A	state B
sample mean	52,236	57,231
sample size	43	49
population standard deviation	6207	6671

The confidence interval is ($ ),($ )

?(Round to the nearest dollar as? needed.)

Answer 1

given data

	state A	state B
sample mean	52,236	57,231
sample size	43	49
population standard deviation	6207	6671

mean of group    A  

mean of group B  

Overall mean of the samples

number of samples in the individual group group =

Total number of sample (n)=43+49=92

No of group (m)=2

Step 1

NOW WITHEN PROPERTY

given that

and

so varience

hence

hence

Step 3 calculate test statistic

test stastistic

step 4     From the table of distribution of probablity we we have to calculate F critical now

so F criticle with respect to degree of freedon (2,92) at

Step 5 conclusion :

Since we found that so we have enough evidence to reject the null hypothesis

hence it is concluded that there is a difference exists between the two given means