When you use Minitab Express, include all relevant output and clearly identify your final answer

by writing a sentence (e.g., "The p value is XX.").

Round all answers to 3 decimal places unless otherwise specified.

Software needed: Minitab Express

Question Set 1: Finding Proportions Under Normal Distributions

In this question set you will use Minitab Express to construct normal distributions to find

different proportions.

A. Using Minitab Express, construct a standard normal distribution to find the area

greater than z = 2. Copy+ paste your distribution here and clearly identify your final

answer. [10 points]

B. Using Minitab Express, construct a normal distribution with a mean of 50 and

standard deviation of 10. Find the area on that distribution greater than x = 70.

Copy+ paste your distribution here and clearly identify your final answer. [10 points]

C. Explain why your answers to A and B are exactly the same. [10 points]

D. SAT-Math scores are normally distributed with a mean of 500 and standard

deviation of 100. Using Minitab Express, compute the percentile for a SAT-Math score

of 560. A percentile the proportion of scores at or below a given score. Copy+ paste

your distribution here and clearly identify your final answer. [10 points]

E. Using Minitab Express, find the z scores that separate the middle 85% of the

standard normal distribution from the outer 15% (7.5% on the left and 7.5% on the

right). Copy+ paste your distribution here and clearly identify your final answer. [10

points]

Question Set 2: Hypothesis Testing

In this question set, we will examine some of the similarities between the randomization

tests we learned about in Lesson 5 and the method we learned in this lesson that applies the

STAT 200 Lesson 7: Common Distributions

Due Tuesday, June 29, 2021

Central Limit Theorem and allows us to use the z distribution to approximate the sampling

distribution. We'll be working with the following scenario:

Research question: Is the mean listing price in the population of all three-bedroom

houses in State College, Pennsylvania different from $300,000?

Data were collected from a representative sample of 40 three-bedroom houses in State

College, Pennsylvania currently listed on Zillow. The observed sample mean was $328,299.

Stat Key was used to conduct a randomization test. The randomization distribution, with the

cut-off set to the observed sample mean, is shown below.

A. What was the p value for the randomization test shown above? Explain how you

determined this. [10 points]

(Hint: This was covered in Lesson 5)

STAT 200 Lesson 7: Common Distributions

Due Tuesday, June 29, 2021

B. Compute the standardized test statistic using the formula below. Use the standard

error from the randomization distribution above. [15 points]

C. Using Minitab Express, construct a standard normal distribution to find the

proportion that is more extreme (i.e., two-tailed probability) than the z test statistic

you computed in part B. Clearly identify your final answer.

[15 points]

(Hint: This should be similar to your answer in part A)

D. Explain why your answers to parts A and C were similar but not exactly the same.

[10 points]