Stat 50
Show your work
Name:_______________________________
1) In a clinical trial of a drug, 2.4% of the 1645 treated subjects experienced headache. Among the 1659 subjects given placebos, 1.5% experienced headache. Us a 0.01 Significance level to test the claim that the incidence of headache is greater among those who use the drug. a) Write the hypothesis
2) A study of the career plans of young women and men sent questionnaires to all 722 members of the senior class in the
College of Business Administration at the University of Illinois. One question asked which major within the business program the student had chosen. Here are the data from the students who responded:
Gender
Major Female Male Total
Accounting 68 56 124
Administration 91 40 131
Economics 5 6 11
Finance 61 59 120
Total 225 161 386 a) Write a hypothesis appropriate for this data b) Test Statistic c) P-value d) Conclusion
3) For married couples with one or more offspring, a demographic study was conducted to determine the effect of the husband’s annual income (at marriage) on the time (in months) between marriage and the birth of the first child. The following table gives the husband’s annual income (INC) and the time between marriage and the birth of the first child
(TIME) for a sample of 11 couples.
INC 5,775 9,800 13,795 4,120 25,015 12,200 7,400 9,340 20,170 22,400 24,210
TIME 16.2 35.0 37.20 9.00 24.40 36.75 31.75 30.00 36.00 30.80 20.00 a) Draw a scatter plot of the data. Comment on the relationship between TIME (Y) on INC(X). b) Which of the two variables is the explanatory variable? c) Determine the equation of the regression line (show calculation) d) Is there a statistically significant linear relationship between TIME and INC? Explain.
Hypothesis: e) Can you suggest a model that would describe the TIME-INC relationship better than a straight line does? f) Predict the time it would take a couple to have their first child if the husband’s annual income is $20,000.

4) A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample data below to construct a 90% confidence interval for u
1
– u
2
where u
1
and u
2 represent the mean for the treatment group and the control group respectively. Test the researcher’s claim by constructing a confidence interval.
Treatment Group Control Group n
1
= 85 n
2
= 75 x
1
= 189.1 s
1
= 38.7
x
s
2
2
= 203.7
= 39.2
a) Hypothesis: b) Construct a 90% Confidence Interval
5) According to menstuff.org, more than 22% of married men have “strayed” at least once during their married lives. A survey of 500 married men results in 122 indicating that they have “strayed” at least once, during their married life. Test the claim made by menstuff.org. Use

= 0.05. a) Hypothesis b) Test Statistic c) P-value d) Conclusion
6) The probability that Jazmin will score above a 90 on a mathematics test is 4/5. What is the probability that she will score above a 90 on exactly three of the four tests this quarter? (Assume trials are independent).
7) 4. There are 38 slots in roulette: 18 black, 18 red and 2 green. Find the odds of a green slot (1pt)
8. A researcher has developed a theoretical model for predicting eye color. After examining a random sample of parents, she predicts the eye color of the first child. The table below lists the eye colors of offspring. Based on her theory, she predicted that 87% of the offspring would have brown eyes, 8% would have blue eyes, and 5% would have green eyes.
Test the claim that the actual frequencies correspond to her predicted distribution.
Brown Eyes Blue Eyes Green Eyes Total
Frequency(observed) 132 17 0 149 a) Hypothesis H o
:
H
1 b) Test Statistic c) Critical Value: d) Conclusion):

9. Two psychologists surveyed 478 children in grades 4, 5, and 6 in elementary schools in Michigan. They asked the students whether their primary goal was to get good grades, to be popular, or to be good at sports. One question of interest was whether boys and girls at his age had similar goals.
Here’s a contingency table giving counts of the students by their goals and gender.
Popular
Goals
Gender
Boy
Girl
Total
Grades
117
130
247
50
91
141
Sports Total
60
30
90
227
251
478
One student is randomly selected, a) What is the probability of selecting a boy and someone who wants to be popular? b) What is the probability that a selected student wants to excel at sports given that we have selected a boy. c) What is the probability of selecting a boy or someone whose goal is to excel at sports.
10) Test the claim that heights of female supermodels vary less than the heights of women in general. The standard deviation of heights of the population of women is 2.5 in. Listed below are the heights (in inches) of randomly selected supermodels (Taylor, Harlow, Mulder, Goff, Evangelista, Auermann, Schiffer, MacPherson, Crawford...
71 71 70 69 69.5 70.5 71 72 70 70 69 69.5 a. Hypothesis: H o
:
H
1
: b. Test Statistic: c. Critical Value: d. Conclusion
11. Assume that weights of men are normally distributed with a mean of 172 lb and a standard deviation of 29 lb. If 20 men have a mean weight greater 180 lb, the total weight exceeds the 3500 lb safe capacity of a particular water taxi.
Find the probability that 20 randomly selected men will have a mean weight that is greater than 180 lb. Based on your results, is this a safety concern?
12 Let the random variable x represent the number of girls in a family of three children. Construct a table describing the probability distribution, then find the mean and standard deviation (hand calculate or use calculator)Hint: write the sample space of the possible outcomes. a) Number of girls in P(x)
in three births
b) Find the mean of the probability distribution.

= c) Find the Standard deviation,
