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(Solved by Expert Tutors) Stat 1? Hypothesis Testing for a Mean Using Summarized Data ? Errors a

A test prep company has developed a new intervention to improve SAT-Verbal scores. They will conduct a hypothesis test to determine if the average SAT-Verbal score of a student who has completed their program is greater than the known national average of 490. The program is very expensive at $12,000 per student.? Use this scenario to answer the following questions.

Write the null and alternative hypotheses __using the appropriate symbols__.? __Step 1__:? Write the null and alternative hypotheses:Null:? ??????????????????? __Step 2__:? Calculate the test statistic:__Step 3____:__? Find the p-value:__Step 4__:? Decide between the null and alternative hypothesis:__Step 5__:? State a real world conclusion:

i. How did decreasing the sample size from 5,000 to 30 change the statistical power of this test?

2 Hypothesis Testing for a Mean Using Raw Data

Answer the following questions using the dataset Spring17Data.MTW. Consider this data to be a sample that is representative of the population of all Penn State World Campus STAT 200 students.?

At the 0.05 alpha level, is there evidence that the mean weight of all Penn State World Campus STAT 200 students is greater than 170 pounds?? Use the five step hypothesis test procedure outlined below.? You can use software for the analysis.? Be sure to include all output!? Remember to show all work and/or output for credit!__Step 1__:? Write the null and alternative hypotheses:__Step 2__:? Calculate the test statistic: __Step 3:__? Find the p-value:__Step 4:__? Decide between the null and alternative hypothesis:__Step 5__:? State a real world conclusion:In part a, is it possible that a Type I or Type II error was committed?? __Explain.__At the 0.05 alpha level, is there evidence that the proportion of students eating breakfast in the population of all Penn State World Campus STAT 200 students is different from 60%? ?Use the five step hypothesis test procedure outlined below. ?If appropriate, apply the normal approximation method. ?Remember to show all work and/or output for credit!__Step 1__:? Write the null and alternative hypotheses:Null:? ???????????????

Alternative:? ?

__Step 2__:? Calculate the test statistic:__Step 3:__? Find the p-value:__Step 4:__? Decide between the null and alternative hypothesis:__Step 5__:? State a real world conclusion:

Construct a 95% confidence interval for the proportion of the population that eats breakfast. ?Use the normal approximation method if appropriate.? Remember to show work and/or output for credit!Explain how the results from both parts a and b could be used to answer the same research question.1? Hypothesis Testing fora Mean Using Summarized Data ? Errors and Power

A test prep companyhas developed a new intervention to improve SAT-Verbal scores. They willconduct a hypothesis test to determine if the average SAT-Verbal score of astudent who has completed their program is greater than the known nationalaverage of 490. The program is very expensive at $12,000 per student.? Use this scenario to answer the followingquestions.

a.??????Write the null and alternative hypotheses __using theappropriate symbols__.?

Ho:?

Ha:?

b.? __In terms of thisscenario__, describewhat a Type I error would look like. (Be sure to apply thisscenario!)?

c.? In terms of thisscenario, describe what a Type II error would look like. (Besure to apply this scenario!)?

d. The researchers used a sample size of n = 5,000 and found asample mean of 495. ?Using the hypothesesfrom part a, and the known population standard deviation of 98, what is thetest statistic?? You may do handcalculations or use software.? ??Rememberto show all work and/or output for credit!

e. ?What is the p-valueassociated with the test statistic you computed in part d?? You can use the t-table or software.? Rememberto show all work and/or output for credit!

f.? Are the results of this study statisticallysignificant? Explain why.

g.? Are the results of this study practicallysignificant?? For example, if you were aparent, would you be convinced that you should spend $12,000 to send your childthrough this program? Explain why or why not.

h.? Run the analyses frompart d again, this time using a sample size of n = 30. ?Use the five step hypothesis testing procedureoutlined below. ?Remember to show all work and/or output for credit!

???????????????????i.???????????__Step 1__:? Write the null andalternative hypotheses:

Null:? ???????????????????

Alternative:?

??????????????????ii.???????????__Step 2__:? Calculate the test statistic:

????????????????iii.???????????__Step 3____:__? Find the p-value:

????????????????iv.???????????__Step 4__:? Decide between the null and alternativehypothesis:__? __

??????????????????v.???????????__Step 5__:? State a real world conclusion:

i. How did decreasing the sample size from 5,000 to 30 changethe statistical power of this test?

2 Hypothesis Testing fora Mean Using Raw Data

Answer the following questions using the dataset Spring17Data.MTW.Consider this data to be a sample that is representative of the population ofall Penn State World Campus STAT 200 students.?

a.??????At the 0.05 alpha level, is there evidence that the mean weightof all Penn State World Campus STAT 200 students is greater than 170 pounds?? Use the five step hypothesis test procedureoutlined below.? You can use software forthe analysis.? Be sure to include alloutput!? Remember to show all work and/or output for credit!

???????????????????????????????i.???????????__Step 1__:? Write the null and alternative hypotheses:

Null:? ???????????

Alternative:?

??????????????????????????????ii.???????????__Step 2__:? Calculate the teststatistic:

????????????????????????????iii.???????????__Step 3:__? Find the p-value:

????????????????????????????iv.???????????__Step 4:__? Decide between thenull and alternative hypothesis:__? __

??????????????????????????????v.???????????__Step 5__:? State a real world conclusion:

b.?????In part a, is it possible that a Type I or Type II error wascommitted?? __Explain.__

3? Hypothesis Testing for a Proportion Using RawData

Answerthe following questions using the dataset Spring17Data.MTW. Consider this datato be a sample that is representative of the population of all Penn State WorldCampus STAT 200 students.?

a.??????At the 0.05 alpha level, is there evidence that theproportion of students eating breakfast in the population of all Penn StateWorld Campus STAT 200 students is different from 60%? ?Use the five step hypothesis test procedure outlinedbelow. ?If appropriate, apply the normalapproximation method. ?Remember to show all work and/or output forcredit!

???????????????????????????????i.???????????__Step 1__:? Write the null and alternative hypotheses:

Null:? ???????????????

Alternative:? ?

??????????????????????????????ii.???????????__Step 2__:? Calculate the teststatistic:

????????????????????????????iii.???????????__Step 3:__? Find the p-value:

????????????????????????????iv.???????????__Step 4:__? Decide between thenull and alternative hypothesis:__? __

??????????????????????????????v.???????????__Step 5__:? State a real world conclusion:

b.?????Construct a 95% confidence interval for the proportion of thepopulation that eats breakfast. ?Use thenormal approximation method if appropriate.?Remember to show work and/oroutput for credit!

c.??????Explain how the results from both parts a and b could be usedto answer the same research question.?

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