Name: ______

Final – Summer 1998

Math 5

Instructions: You must answer questions one and two. From the remainder of the questions you must choose 2 to answer. The total number of questions you will be answering will be 4! Please show all work clearly and box your final answer. Read each question carefully before you answer it. Good luck!

1. The following are the ages of 30 Oscar-Winning best actresses:

28, 31, 32, 32, 35, 36, 37, 37, 38, 39, 39, 40, 40, 41, 42,

42, 43, 43, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 55, 56

Answer the following questions with reference to the sample data.

a) Is the data qualitative or quantitative?______

b) Calculate x, s, Q1, Q3, x. Show the formula that you used and how you

plugged the numbers in, as well as intermediate steps in arriving at the final

answers. (x = 1262 & x2 = 54556)

c) Give the minimum and maximum of the sample.

#1 continued

1.d) Show the shape of the sample data using a histogram (use 12 classes), boxplot,

or a stem and leaf plot (use 2 stems for each). If you choose a histogram, you

must show the frequency table and the derivation of the class width and classes,

and if you use a stem and leaf do not forget to label the stem and leaf units.

e) What is the shape of the data? (Right skewed, Left Skewed or Bell Shaped)

______

f) Give a 99% confidence interval for the population mean if  = 9.04

g) Give a 99% confidence interval for the population mean if  is unknown.

h) Test the hypothesis, at  = 0.05, that the average age for winning an Oscar for

best actress is less than 42. Be sure to state explicitly the null and alternative

hypotheses, the critical value, the test statistic and your conclusion both

technically and in layman's terms.

2. It is known that there is a 50/50 chance of having a boy or a girl when a single baby is

born.

a) What type of data would you consider birth records if they record only the

gender of the child? (Qualitative – Nominal/Ordinal or Quantitative –

Interval/Ratio. Choose Qualitative or Quantitative and one of the subtypes

listed after it.)

______

b) In the next 10 births, what is the exact probability that 8 or 9 girls are born?

Be sure to show exactly how you arrive at the probability, including any

formulas and work done – just an answer is not acceptable. An approximation

is not acceptable.

c) Using the normal approximation, what is the probability that between 8 and 9

girls are born in the next 10 births? (Set up the problem and get a probability

only if the approximation is valid. If you do not solve the problem state the

violation. Show all work that would be used to achieve a final answer. Don't

forget that there is a 50/50 chance of getting a boy or a girl.)

#2 continued

2.d) A sample shows that in 150 births there were 84 girls born. Find a 90%

confidence interval for the true population proportion.

e) Some social scientists claim that actual proportion of girls born is more than

50%. Using the sample data collected for part d) test this claim at a 0.1

significance level. Be sure to state explicitly the null and alternative

hypotheses, the critical value, the test statistic and your conclusion both

technically and in layman's terms.

In questions 3 through 6 you only have to answer 2 questions. Don't answer all of them.

3. The accompanying table lists age and cholesterol level reduction of 15 men in a study

of the importance of diet and exercise in the reduction of cholesterol levels in men. It

is the desire of the doctors to find a relationship between age and cholesterol. Based

on the results answer the questions that follow.

Age / 45 / 43 / 46 / 49 / 50 / 37 / 34 / 30 / 31 / 26 / 22 / 58 / 60 / 52 / 27
Cholesterol
Reduction / 30 / 52 / 45 / 38 / 62 / 55 / 25 / 30 / 40 / 17 / 28 / 44 / 61 / 58 / 45

a) Draw a scatter plot of the data. Does the scatter plot show a linear

relationship, and if so is it positive or negative. If it doesn't state that fact.

b) Mathematically, show the strength of the relationship between age and

cholesterol level reduction. Show your work in arriving at the mathematical

measure of relationship. (age = 610, cholesterol = ?? ,

age*cholesterol = 27,144 , age2 = 26,834 , cholesterol2 = 29,186)

#3 continued

3.c) Test the hypothesis that there is statistically significant positive correlation

between age and cholesterol level reduction at  = 0.05. Be sure to state

explicitly the null and alternative hypotheses, the critical value, the test statistic

and your conclusion both technically and in layman's terms.

d) Give the regression equation that describes the data. Think carefully about the

x and y values. Show the equations used to obtain the equation and the

appropriate work – don't overwork yourself!

e) Predict what the cholesterol level reduction for a 42 year old man.

4. The Menlo Park Electronics Company makes switching devices for traffic signals.

One batch of 10 switches includes 2 that are defective. If 2 switches are randomly

selected without replacement, let the random variable x represent the number that are

defective.

a) Complete the probability density function. Show the work used to complete it.

x / 0 / 1 / 2
P(x)

b) Find the mean of the random variable x. Show all work used to arrive at your

answer, including a formula.

c) Find the standard deviation of the random variable x. Show all work used to

arrive at your answer, including a formula.

5. The lengths of pregnancies are normally distributed with a mean of 268 days and a

standard deviation of 15 days. Answer the following questions concerning this normal

distribution.

a) If we stipulate that a baby is premature if the length of pregnancy is below the

4th percentile, find the length that separates premature babies from those who

are not premature.

b) If 1 pregnant woman is randomly selected, find the probability that her length

of pregnancy is less than 260 days.

c) If 25 randomly selected women are put on a special diet just as they become

pregnant, find the probability that their lengths of pregnancy have a mean that is

less than 260 days (assuming that the diet has no effect).

6) A consumer service research group studied 50 new car dealers in a city. Of the 50

surveyed, 26 had good service records and of these 16 had been in service for 10 years

or more. Of all the dealers, 30 had been in service less than 10 years.

a) Create a contingency table for the information given.

b) Find the probability of randomly choosing a dealership that has good service or

has been in service less than 10 years.

c) If a dealer has been in service less than 10 years what is the probability that they

will have a bad service record.

d) Find the probability of choosing a dealer with bad service.

e) Find the probability of choosing a dealership that has bad service and has been

in service for 10 or more years.