Statistics Problems: Pharmaceutical Sales, Food Consumption, Gender of Athletic Coaches, Labor Stati

Pharmaceutical Sales - 5 Number Summary and Boxplot

Task:

(1) Pharmaceutical Sales - 5 Number Summary and Boxplot

Annual sales, in millions of dollars, for 21 pharmaceutical companies are as follows:

8,408

1,374

1,872

8,879

2,459

11,413

608

14,138

6,452

1,850

2,818

1,356

10,498

7,478

4,019

4,341

739

2,127

3,653

5,794

8,305

Provide a five-number summary.

What is the mean?

What is the mode?

Does the data contain outliers? If so, what are they?

Draw a boxplot.

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(2) Food Consumption - Least Squares Regression

During World War II, there was a scarcity of food rich in fat (meat, butter, eggs, etc.) in Norway (and other countries). Along with a decline in the consumption of fat, a decline in the death rate from atherosclerosis was also observed. (Atherosclerosis is the formation of fatty deposits on the walls of the arteries, which can lead to heart disease and stroke.) The following table gives the consumption of fat in kilograms per year per person (x) and the number of deaths from atherosclerosis per 100,000 people in a year (y) for Norway from 1938 to 1947. Draw a scatterplot. Visually estimate and sketch the best fit line. Other information you might find useful:

Mean standard deviation correlation

Rate (x) 11.61 2.16459 .886

Deaths (y) 25.85 2.66218

Use the given information and formulas given in your textbook to calculate the least squares coefficients a and b. Write the equation of the linear regression line.

If the consumption of fat were 13 kilograms per year per person, what would be the annual death rate (for Norway) due to atherosclerosis?

Year 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947

Rate (x) 14.4 16.0 11.6 11.0 10.0 9.6 9.2 10.4 11.4 12.5

Deaths (y) 29.1 29.7 29.2 26.0 24.0 23.1 23.0 23.1 25.2 26.1

(3) Gender of Athletic Coaches - Two Way Table and Segmented Bar Graph Qualifications of male and female head and assistant college athletic coaches were compared in a recent paper. They were classified according to the number of years of coaching experience. The data is given in the following table.

Years of Experience

1-6 7-12 13 or more

Male 561 843 811

Female 484 402 258

What type of variables are years of experience? _______________________

How many respondents have 1-6 years of experience? _______________________

How many have 7-12 years of experience? _______________________

How many have more than 13 years of experience? _______________________

How many males were surveyed? _______________________

How many females? _______________________

What percentage of women have 1-6 years of experience? _______________________

What percentage of women have 7-12 years of experience? _______________________

What percentage of women have 13 years of experience? _______________________

What percentage of men have 1-6 years of experience? _______________________

What percentage of men have 7-12 years of experience? _______________________

What percentage of men have 13 years of experience? _______________________

Present these percentages in the form of a segmented bar graph.

Write a brief description of the relationship between years of coaching experience and gender.

(4) Labor Statistics- Normal Distribution

According to the Bureau of Labor Statistics, the average weekly pay for a US production worker was $441.84. (The World Almanac, 2000). Assume the available data indicate that production worker wages were normally distributed with a standard deviation of $90. What is the probability that a worker earned between $400 and $500 per week? How much did a production worker have to earn per week to be in the top 20% of wage earners? For a randomly selected production worker, what is the probability the worker earned less than $250 per week?

(5) Mean Weight of a Package of Cookies- Central Limit Theorem

Assume the weights of all packages of a certain brand of cookies are normally distributed with a mean of 32 ounces and a standard deviation of 0.3 ounce. A random sample of 20 packages of this brand of cookie were taken.

Use the Central Limit Theorem to find the standard deviation of the sample (standard error).

Draw a well labeled sketch of this sampling distribution.

Find the probability that the mean weight,