Problem 1 (10 points)

Shown below is a histogram representing the income of the employees of a local fortune 500 company.

Variable N Mean Median TrMean StDev

Annual S 1000 101165 68734 88756 104296

Variable Minimum Maximum Q1 Q3

Annual S 55 812679 29194 141138

A representative of this company then released the following statement:

It is a great day for our company when we can finally say that more than half of our workforce is making over $100,000.00 per year. When the average salary is this high we can without reservation claim to be the greatest company to work for in this great nation.

1. Do you believe this statement to be an accurate representation of the statistics shown above? Explain your conclusions.

1. How could you change this statement to accurately portray this information?

Problem 2 (12 points)

McDonalds is known worldwide for its ability to provide a quality product in a timely manner. Below is a data set that represents the time that it takes to fill a late night burger crave measured in seconds.

37	42	56	12	15	35
16	47	53	17	23	19

a. Find the mean, median and mode for this data set.

b. Find the range, IQR and standard deviation for this data set.

c. Would it be unusual to find an order that took 60 seconds to fill? How do you know?

Problem 3 (12 points)

An unprepared student is about to take his first test of the semester. He is told that his test will be composed of 20 multiple choice questions, each with 4 possible answers, only one of which is correct.

1. What is the probability that the unprepared student randomly guesses at the correct response on ONE of the questions and gets the question correct?

1. What is the probability that the unprepared student randomly guesses at the correct response on ONE of the questions and gets the question wrong?

1. What is the probability that the student guesses at all 20 questions and gets at least one questions correct?

Problem 4 (9 points)

Spell-checking software catches nonword errors which result in a string of letters that is not a word, as when the is type teh. When undergraduates are asked to write a 250 word essay (without spell checking), the number X of nonword errors has the following distribution:

Errors (X)	0	1	2	3	4
Probability	0.3	0.25	0.2	0.17

a.In the table shown above the probability of exactly 4 errors is not given. Using what you know about probability distributions, what is the probability of exactly 4 errors?

b.What is the probability of at least 1 nonword error? c.Find the expected value of this distribution. How many nonword errors can you expect from a typical paper written under the previously mentioned conditions?

Problem 5 (8 points)

Researchers conducted a study to determine whether there were significant differences in graduation rates between medical students admitted through special programs (such as affirmative action) and medical students admitted through the regular admissions criteria. It was found that the graduation rate was 84% for the medical students admitted through special programs.

a. If 15 of the students from the special programs are randomly selected, find the probability that exactly 12 of them graduated.

b. If 15 of the students from the special programs are randomly selected, find the probability that fewer than 10 of them graduated.

Problem 6 (16 points)

Assume that the lengths of pregnancies are normally distributed with a mean of 280 days and a standard deviation of 7 days.

a. What is the probability that a randomly selected mother will have a pregnancy lasting longer than 300 days?

b. What is the probability that a randomly selected mother will have a pregnancy lasting shorter than 268 days?

c. What is the probability that a randomly selected mother will have a pregnancy lasting between 272 and 284 days?

d. Find the 95th percentile for the lengths of pregnancies.

Problem 7 (5 points)

A nationwide poll of 1000 likely voters by the Public Policy Polling group indicated that 53% are in favor of passing Amendment 1 to the North Carolina State Constitution.

a. Find a 95% confidence interval for the proportion of all likely votes that would vote in favor of Amendment 1. Interpret this interval.

b. Based on this sample is it still REASONABLY possible that Amendment one would not pass? Explain your conclusions.

Problem 8 (18 points)

An individual wanted to determine the relation that might exist between speed and miles per gallon of an automobile. Let X be the average speed of a car on the highway measured in miles per hour and let Y represent the miles per gallon of the automobile. The following data is collected:

X	50	55	55	60	60	62	65	65
Y	28	26	25	22	20	20	17	15

a. In the space below, draw a scatterplot of the bivariate data set.

b. What is the value for r? Interpret this value, would you say that the correlation is positive or negative? Strong or Weak? How do you know?

c. From the regression equation given above, what value is the slope of the line? Interpret this slope, what does it tell us about the relationship between average speed and miles per gallon?

d. Predict the miles per gallon of a car traveling 63 miles per hour.

e. Predict the average speed of a car whose fuel mileage is 23 miles per gallon.

f. Find r squared. What does this statistic tell us about between average speed and miles per gallon?

Problem 9 (15 points)

In one study of smokers who tried to quit smoking with nicotine patch therapy, of the 100 that were surveyed, 47 were smoking one year after the treatment and 53 were not smoking one year after the treatment. Use a 0.05 level of significance to test the claim that among smoking Americans who try to quit with nicotine patch therapy that more than half are smoking a year after the treatment.

a. Give the appropriate null and alternative hypotheses statements.

b. Determine the type of test (one or two tailed). Also determine the proper alpha level.

c. Find the appropriate test statistic and state the p-value.

d. What is your decision about the null hypothesis?

e. State your final conclusions in non-symbolic English.