Answer the following questions showing all work. Full credit will not be given t

Question

Answer the following questions showing all work. Full credit will not be given to answers without work shown. If you use Minitab Express include the appropriate output (copy + paste) along with an explanation. Output without explanation will not receive full credit. Round all answers to 3 decimal places. If you have any questions, post them to the course discussion board. **Please use equation editor to communicate correct notation and mathematical notation.

1. For each of the following scenarios, which of the following hypothesis tests is most appropriate: one sample proportion, one sample mean, two independent proportions, two independent means, or two paired (dependent) means? Explain why. [24 points]

A. Penn State’s College of Science would like to know if biology majors and physics majors differ in terms of whether or not they have had a high school chemistry course.

B. A particular TV show would like to know if the average age of their viewers is less than 22 years old.

C. Penn State’s Department of Statistics wants to know if applicants to its major have SAT-Math scores that are higher than their SAT-Verbal scores. They take a simple random sample of 40 applicants and record each individual’s SAT-Math and SAT-Verbal scores.

D. Students at Penn State and Michigan State are arguing over which university’s students are faster. They take a random sample of 25 students from each university and time how long it takes them to run 400 meters.

E. We know that in the population of all Penn State World Campus students 18.6% have military experience. An instructor at Penn State Harrisburg wants to know if the proportion of students at Penn State Harrisburg is different from 18.6%. She takes a random sample of 100 Penn State Harrisburg students and records whether or not each student has military experience.

F. A pharmaceutical company wants to compare the LDL cholesterol levels of patients who have taken two different drugs (Drug A and Drug B). They randomly assign 30 patients to receive Drug A and 30 patients to receive Drug B. After taking 90 days they measure each patient’s LDL cholesterol level.

2. I want to compare STAT 200 students’ scores on the Lesson 1 Quiz and the Lesson 2 Quiz. In a random sample of 50 students, the mean difference was 0.350 points with a standard deviation of 1.780 points. Scores tended to be higher on the Lesson 1 Quiz. Use Minitab Express to answer the following questions. You will have to enter in these statistics as “summarized data” in Minitab Express. [20 points]

A. Construct a 95% confidence interval for the mean difference between the scores on the two quizzes.

B. Use the five-step hypothesis testing procedure to test the alternative hypothesis that scores are different on the two quizzes.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Explanation / Answer

Solution:

1. a) Single mean test which is one tailed[t test], since variable under study is measured as quantitative and on ratio scale.
b) Two independent means test which is one tailed[t test], since variable under study is measured as quantitative and on interval scale.
c) Two independent means test which is one tailed [t test], since variable under study is measured as quantitative and on interval scale.
d) Two independent means test which is one tailed [t test], since variable under study is measured as quantitative and on interval scale.
e) Single proportion test which is two tailed[z test], since variable under study is measured as categorical and on nominal scale.
f)Two paired (dependent) means test which is one tailed [t test], since variable under study is measured as quantitative and on interval scale.
g) Two independent means test which is two tailed [t test], since variable under study is measured as quantitative and on ratio scale.
h) Two proportion test which is two tailed [z test], since variable under study is measured as categorical and on nominal scale.
i) Two independent means test which is two tailed [t test], since variable under study is measured as quantitative and on ratio scale.
j) Two paired (dependent) means test which is one tailed [t test], since variable under study is measured as quantitative and on interval scale.

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