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MS 5318 Homework # 2

Due: Thursday, Feb 16, 2022

Instructions:

•    Submit Homework Assignments individually.

•    For short-answer questions, you may receive partial credits by showing all work even if your final answer is incorrect.

1. (5 pts) Do poets die young?  According to William Butler Yeats, “She is the Gaelic muse, for she gives inspiration to those she persecutes. The Gaelic poets die young, for she is restless, and will not let them remain long on earth.” One study designed to investigate this issue examined   the age at death for writers from different cultures and genders.  Three categories of writers      examined were novelists, poets, and nonfiction writers.  The ages at death for female writers in these categories from North America are given in poets.xls. Most of the writers are from the United States, but Canadian and Mexican writers are also included

Does the mean age at death differ among the three groups?  Run the appropriate procedure and summarize the findings. Use a significance level a = 0. 05. In your submission, include the Excel output tables NOT the original data.

2.  (5pts) A particular paperback mystery book is published with a choice of three different pictures on the cover: a photograph of the actor playing the main character in the movie version of the book, a drawing of the mansion where the story in the book takes place, or an embossed  graphic of the murder weapon.  A certain bookstore keeps copies of this book with each of the   pictures on the cover on its racks.  To test the hypothesis that sales of this book are equally divided among the three choices, a simple random sample of 120 purchases of this book is obtained. The numbers are displayed in the table below:

Picture on the cover

Total

Photograph

Drawing

Embossed graphic

31

47

42

120

Run the appropriate procedure to test the null hypothesis that sales of this book are equally divided among the three choices.  Report the results and the conclusion of your hypothesis  tests. Use a = 0.05.

3. (5pts)  The students in a statistics class are categorized by gender and by the year in school. The numbers obtained are displayed below:

                                                   Year in school

Gender         Freshman         Sophomore         Junior         Senior

Male                 5                       4                   15              19

Female             25                     23                  13              10

Suppose we wish to test the null hypothesis that there is no association between the year in school and gender.  What are the results and the conclusion of the test?  Use a = 5%.

4. (5pts) A producer of fertilizer fills bags using an automated process. When the process is in control, the mean weight of the bags is μ=50 kilograms and the standard deviation of the weights is σ=2.4 kilograms. Each hour, 30 filled bags are selected at random and the average weight is computed. The quality control manager set the control limits for the sample average weight to be [48.98, 51.02]. If the sample mean falls outside the control limits, the manager has to stop the process and have the filling machine calibrated. If the process is in control, what is the probability that the average weight will be within the control limits? Note: use central limit theorem.