I need help with these questions.

5.You may need to use the appropriateappendix tableortechnologyto answer this question.

Consider the following hypothesis test.

H₀:25

H_a:> 25

A sample of 40 provided a sample mean of26.8. The population standard deviation is 6.

(5.A) Find the value of the test statistic. (Round your answer to two decimal places.)

(5.B)Find thep-value. (Round your answer to four decimal places.)

p-value =

(5.C)At= 0.01,state your conclusion.

a)RejectH₀. There is sufficient evidence to conclude that> 25.

b)RejectH₀. There is insufficient evidence to conclude that> 25.

c)Do not rejectH₀. There is sufficient evidence to conclude that> 25.

d)Do not rejectH₀. There is insufficient evidence to conclude that> 25.

(5.D)State the critical values for the rejection rule. (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic _______

test statistic _______

State your conclusion.

a)RejectH₀. There is sufficient evidence to conclude that> 25.

b)RejectH₀. There is insufficient evidence to conclude that> 25.

c)Do not rejectH₀. There is sufficient evidence to conclude that> 25.

d)Do not rejectH₀. There is insufficient evidence to conclude that> 25.

6.Individuals filing federal income tax returns prior to March 31 received an average refund of $1,049. Consider the population of "last-minute" filers who mail their tax return during the lastfive daysof the income tax period (typicallyApril 10toApril 15).

(6.A) A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection ofH₀will support the researcher's contention.

a)H₀:> $1,049

H_a:$1,049

b)H₀:$1,049

H_a:> $1,049

c)H₀:$1,049

H_a:< $1,049

d)H₀:< $1,049

H_a:$1,049

e)H₀:= $1,049

H_a:$1,049

(6.B) For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience, a population standard deviation of= $1,600may be assumed.

What is the test statistic? (Round your answer to two decimal places.)

=

What is thep-value?(Round your answer to four decimal places.)

p-value =

(6.C)

At= 0.05,what is your conclusion?

a)RejectH₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,049.

b)Do not rejectH₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,049.

c)Do not rejectH₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,049.

d)RejectH₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,049.

(6.D) Repeat the preceding hypothesis test using the critical value approach.

State the null and alternative hypotheses.

a)H₀:> $1,049

H_a:$1,049

b)H₀:$1,049

H_a:> $1,049

c)H₀:$1,049

H_a:< $1,049

d)H₀:< $1,049

H_a:$1,049

e)H₀:= $1,049

H_a:$1,049

Find the value of the test statistic. (Round your answer to two decimal places.)

=

State the critical values for the rejection rule. (Use= 0.05. Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic _____

test statistic _____

State your conclusion.

a)RejectH₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,049.

b)Do not rejectH₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,049.

c)Do not rejectH₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,049.

d)RejectH₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,049.

7.Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of15minutesor less. If a longer mean survey time is necessary, a premium rate is charged. A sample of35 surveysfrom a particular client provided the survey times shown in the file named Fowle. Based upon past studies, the population standard deviation is assumed known with=4minutes.Is the premium rate justified for this client?

17 11 12 23 20 23 15

16 23 22 18 23 25 14

12 12 20 18 12 19 11

11 20 21 11 18 14 13

13 19 16 10 22 18 23

(7.A) Formulate the null and alternative hypotheses for this application.

a)H₀:> 15

H_a:15

b)H₀:< 15

H_a:15

c)H₀:15

H_a:< 15

d)H₀:= 15

H_a:15

e)H₀:15

H_a:> 15

(7.B)Compute the value of the test statistic. (Round your answer to two decimal places.)

=

(7.C)What is thep-value? (Round your answer to four decimal places.)

p-value =

(7.D)At= 0.01,what is your conclusion?

a)Do not rejectH₀. There is sufficient evidence to conclude that the premium rate should be charged.

b)Do not rejectH₀. There is insufficient evidence to conclude that the premium rate should be charged.

c)RejectH₀. There is sufficient evidence to conclude that the premium rate should be charged.

d)RejectH₀. There is insufficient evidence to conclude that the premium rate should be charged.

8.At a university the historical mean of scholarship examination scores for freshman applications is800. A historical population standard deviation=150

is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.

(8.A)State the hypotheses.

(8.B)What is the 95% confidence interval estimate of the population mean examination score if a sample of90applications provided a sample meanx=832?

(8.C)Use the confidence interval to conduct a hypothesis test. Using= 0.05,

what is your conclusion?

(8.D)What is the test statistic? What is thep-value?

9.Consider the following hypothesis test.

H₀:=14

H_a:14

A sample of 58 provided a sample meanx=13and a sample standard deviations=6.7.

(9.A)Compute the value of the test statistic.

(9.B)Use thetdistribution tableto compute a range for thep-value.

(9.C)At= 0.05,what is your conclusion?

(9.D)What is the rejection rule using the critical value? What is your conclusion?