Question

Given two independent random samples with the following results:

n1=10 x‾1=90 s1=11    n2=15 x‾2=117 s2=22

Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are not equal and that the two populations are normally distributed.

Step 1 of 3: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 3: Find the standard error of the sampling distribution to be used in constructing the confidence interval. Round your answer to the nearest whole number.

Step 3 of 3: Construct the 90% confidence interval. Round your answers to the nearest whole number.

Answer 1

Solution-

step 1 ) critical value-

tc = 1.714

Step 2) Standard Error-

Se = 7 ...... (rounded to whole number)

◆ Calculation -

Step 3) Confidence Interval

90% confidence interval for the difference between the population means μ1​−μ2​ is −38 < μ1​−μ2​ < −16, which indicates that we are 90% confident that the true difference between population means is contained by the interval (−38,−16).

....(rounded to whole number)

◆ calculations -