Provided below are summary statistics for independent simple random samples from two populations. Use the nonpooled t-test and the nonpooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.
X1 = 11, S1 = 5, n1 = 25, x2 = 10, S2 = 4, n2 = 20
A) What are the correct hypotheses for aright-tailed test? α = 0.05
i. Compute the test statistic.
ii. Determine the P-value.
B) The 90% confidence interval is from to

Using the t-distribution, we have that:

a)

i) The test statistic is t = 0.746.

ii) The p-value is of 0.2299.

b) The 90% confidence interval is from -1.25 to 3.25.

Item a:

For a right-tailed test, we test if is greater than , hence:

The standard errors are:

The distribution of the difference has mean and standard error given by:

We have the standard deviation for the samples, hence, the t-distribution is used.

The test statistic is given by:

In which is the value tested at the null hypothesis.

Hence:

The test statistic is t = 0.746.

The p-value is found using a t-distribution calculator, with t = 0.746, 25 + 20 - 2 = 43 df and 0.05 significance level.

Item b:

The critical value for a 90% confidence interval with 43 df is .

The interval is:

Hence:

The 90% confidence interval is from -1.25 to 3.25.

A similar problem is given at link

42

step-by-step explanation:

256/6=42

8y^50

step-by-step explanation: