STP 226 Test 3
NAME:______ASU ID: ______
TU 9:15 or 12:15
STP 226 SPRING 2001
Exam 3
There are 7 questions on this test adding up to 100 points plus a 5 point bonus. Read all the questions carefully.
Honor Policy: By signing below you confirm that you have neither given nor received any unauthorized assistance on this exam.
Signature: ______
Date: ______
GOOD LUCK!
Directions: Please read the questions carefully and place your answer in the space
provided at the end of each question. Show working where necessary.
Circle the letter of the correct answer for multiple choice questions.
1.(5)The mean annual income for adult women in one city is $28,520 and the standard deviation of the incomes is $5,190. The distribution of incomes is skewed to the right. For samples of size 50, which of the following statements best describes the sampling distribution of the mean?
a. is normally distributed.
b.Nothing can be said about the distribution of .
c.The distribution of is skewed to the right.
d. is approximately normally distributed.
2.(5)In 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from 1990 mean of 9.4 minutes. The hypotheses are:
H0 : = 9.4 minutes
Ha : 9.4 minutes
Suppose that the results of the sampling lead to non-rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes.
a.Type I errorb.Correct decisionc.Type II error
3.(20)A laboratory test tested 70 chicken eggs and found that the mean amount of cholesterol was 204 milligrams. Assume that = 10.6 milligrams. Construct a 95 percent confidence interval for the true mean cholesterol content, , of all such eggs.
4.(10)The weekly earnings of students in one age group are normally distributed with a standard deviation of 61 dollars. A researcher wishes to estimate the mean weekly earnings of students in this age group. Find the sample size needed to assure with 98 percent confidence that the sample mean will not differ from the population mean by more that 2 dollars.
5.(20)A researcher wants to check the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 35 such cases from court files and finds that = 16.7 months. Assume that the population standard deviation is 7 months. Test the hypothesis that = 18.7 at the 0.05 significance level.
6.(20)A researcher was interested in comparing the GPAs of students at two different colleges. Independent random samples of 8 students from college A and 13 students from college B yielded the following GPAs.
College A / College B3.7, 3.2, 3.0, 2.5, 2.7, 3.6, 2.8, 3.4 / 3.8, 3.2, 3.0, 3.9, 3.8, 2.5, 3.9
2.8, 4.0, 3.6, 2.6, 4.0, 3.6
Do the data provide sufficient evidence to conclude that the mean GPA of students at college A differs from the mean GPA of students at college B? Perform a pooled t-test at the 10% significance level.
(Note: 1 = 3.1125, 2 = 3.4385, s1 = 0.4357, s2 = 0.5485)
7.(20)The table below shows the weights of four subjects before and after following a particular diet for two months.
Subject / A / B / C / DBefore / 191 / 185 / 165 / 192
After / 184 / 176 / 163 / 190
Differences
Do the data suggest that the diet is effective in reducing weight? Perform a paired t-test at the 5% significance level.
Bonus(5) Based on a sample of 35 randomly selected years, a 90% confidence interval
for the mean annual precipitation in one city is from 43.3 inches to 46.7 inches. Find the margin of error.
a.There is not enough information to find the margin of error.
b.0.47 inchesb.3.4 inchesd.1.7 inches
END OF TEST.
1
STP 226 TEST 3 SPRING 2001
Copyright Arizona State University Department of Mathematics