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

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!

the homeowners insurance cost for a 115,000 wood frame house is 80,500.

step-by-step explanation:

it is given that the coverage rate for wood frame house is 0.7.

the value of wood frame house is 115,000.

.

homeowners insurance cost for a 115,000 wood frame house is

therefore the homeowners insurance cost for a 115,000 wood frame house is 80,500.