Given the following information about a hypothesis test of the difference between two means based on independent random samples, which one of the following is the correct rejection region at a significance level of .05? Assume that the samples are obtained from normally distributed populations having equal variances. HA: μA > μB, = 12, = 9, s1 = 5, s2 = 3, n1 = 13, n2 = 10.A. Reject H0 if Z > 1.96B. Reject H0 if Z > 1.645C. Reject H0 if t > 2.08D. Reject H0 if t > 1.782E. Reject H0 if t > 1.721

Null hypothesis:

Alternative hypothesis:

Since we dpn't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

(1)

Now we need to find the degrees of freedom given by:

And now since we are conducting a right tailed test we are looking ofr a value who accumulates 0.05 of the are on the right tail fo the t distribution with df =21 and we got:

And for this case the rejection zone would be:

E. Reject H0 if t > 1.721

Step-by-step explanation:

Data given and notation

represent the mean for 1

represent the mean for 2

represent the sample standard deviation for 1

represent the sample standard deviation for 2

sample size for the group 1

sample size for the group 2

t would represent the statistic (variable of interest)

significance level provided

Develop the null and alternative hypotheses for this study

We need to conduct a hypothesis in order to check if the mean for group A is higher than the mean for B:

Null hypothesis:

Alternative hypothesis:

Since we dpn't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

(1)

Now we need to find the degrees of freedom given by:

And now since we are conducting a right tailed test we are looking ofr a value who accumulates 0.05 of the are on the right tail fo the t distribution with df =21 and we got:

And for this case the rejection zone would be:

E. Reject H0 if t > 1.721

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step-by-step explanation:

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the answer is a.

step-by-step explanation:

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