1. I took a sample of the grade point averages for students in my class. For 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89. The standard error for the sample was:
(3 marks)
2. The heights (in inches) of adult males in Bhutan are believed to be normally distributed with mean µ. The average height of a random sample of 25 Bhutanese adult males is found to be = 69.72 inches and the standard deviation of the 25 heights is found to be s = 4.15.
A 90% confidence interval for µ is (3 marks)
3. A local farmer is interested in comparing the yields of two varieties of tomatoes. In an experimental field, he selects 20 locations and assigns 10 plants from each variety at random to the locations. He determines the yield per plant (in pounds). The mean yield for plants of variety 1 was 16.3 pounds with a standard deviation of 3 pounds. The mean yield for plants of variety 2 was 18.4 pounds with a standard deviation of 4 pounds. What is the standard error of the difference in sample means? (3 marks)
4. The water diet requires you to drink two cups of water every half hour from when you get up until you go to bed, but eat anything you want. Four adult volunteers agreed to test this diet. They are weighed prior to beginning the diet and six weeks after. Their weights in pounds are:
Person 1 2 3 4 mean s.d.
Weight before 180 125 240 150 173.75 49.56
Weight after 170 130 215 152 166.75 36.09
Difference 10 -5 25 -2 ?? 13.64
What is the test statistic? (3 marks)
5. A researcher wants to know if the average time in jail for robbery has increased from what it was several years ago when the average sentence was 7 years. He obtains data on 400 more recent robberies and finds an average time served of 7.5 years. If we assume the standard deviation is 3
years, what is the P-value of the test? (5 marks)
6. What is the P-value for a test of the hypotheses H0: μ = 10 against Ha: μ ≠ 10 if the calculated statistic is z = 2.56? (3 marks)
7. In a discussion of mathematics scores in the civil service exams, someone comments: “Because only a minority of students studying abroad takes the test, the scores overestimate the ability of a typical student who studies abroad. I think that if all students who studied abroad took the test the mean score would be no more than 450”. You decided to test this claim and gave the mathematics exams to a group of 500 graduates who studied abroad. These students had a mean score of 461 and a SD of 100. Is this good evidence against this claim? Find the p value. (5 marks)
8. A report states that on average, Indian subscribers with 3G phones spent an average of 8.3 hours per month listening to music on their cell phones. Suppose we want to determine a 955 confidence interval for the Bhutanese average and draw the following random sample of size 8 from the Bhutanese population of 3G subscribers: 5,6,0,4,11,9,2,3. Set a 95% confidence interval for the Bhutanese sample? (5 marks)
9. Is an accident likely to happen when using a cell phone while driving? A study of 699 drivers who were using cell phones when they were involved in a collision examined this question. These drivers made 26.798 phone calls during a 14 month study period. Each of the 699 collision were3 classified in various ways. Here are the numbers for each day of the week;
Number of collisions by day of the week
sun mon tue wed thu fri sat Total
20 133 126 159 136 113 12 699
Are the accidents equally likely occur on each day of the week? (7 marks)
10. A professor is interested to learn whether there is a significant difference between the achievement levels of two populations of students at two different colleges. He collects performance data by administering the same midterm exam to one class at each college. He randomly selects 30 students from each class and gets the following results:
College 1 College 2 Difference in
Student Number Test Score Student Number Test Score Test Scores
1 20 1 25 -5
2 16 2 22 -6
3 22 3 30 -8
4 26 4 21 5
5 26 5 29 -3
6 27 6 24 3
7 15 7 24 -9
8 20 8 19 1
9 25 9 22 3
10 17 10 23 -6
11 18 11 26 -8
12 16 12 20 -4
13 15 13 24 -9
14 17 14 22 -5
15 18 15 22 -4
16 15 16 23 -8
17 18 17 26 -8
18 19 18 30 -11
19 22 19 28 -6
20 19 20 30 -11
21 19 21 18 1
22 19 22 20 -1
23 26 23 24 2
24 21 24 19 2
25 20 25 25 -5
26 19 26 20 -1
27 27 27 26 1
28 25 28 30 -5
29 27 29 19 8
30 18 30 19 -1
Sample Average 20.40 23.67 -3.27
Sample Standard Deviation 3.96 3.74 4.95
Perform a test of the hypothesis that there is no significant difference between the population mean test scores at the two schools, using . (7 marks)
11. If, in a sample of size selected from an underlying normal population, the sample mean is and the sample standard deviation is , what is the value of the t-test statistic if we are testing the null hypothesis H0 that ?
(5 marks)
12. The manager of the credit department for BOB would like to determine whether the average monthly balance of credit card holders is equal to 75. An auditor selects a random sample of 100 accounts and finds that the average owed is 83.40 with a sample standard deviation of 23.65.
Using the 0.05 level of significance, should the auditor conclude that there is evidence the average balance is different from 75? (5 marks)
13. . A manufacturer of plastics wants to evaluate the durability of rectangularly molded plastic blocks that are to be used in furniture. A random sample of 50 such blocks is examined and it gives a mean of 267.6 and a SD of 24.2. Using the 0.05 level of significance, is there evidence that the average hardness of the plastic blocks exceeds 260? (5 marks)
14. The operations manager at a light bulb factory wants to determine if there is any difference in the average life expectancy of bulbs manufactured on two different types of machines. The process standard deviation of Machine I is 110 hours and of Machine II is 125 hours. A random sample of 25 light bulbs obtained from Machine I indicates a sample mean of 375 hours, and a similar sample of 25 from Machine II indicates a sample mean of 362 hours.
Using the 0.05 level of significance, is there any evidence of a difference in the average life of bulbs produced by the two types of machines. (7 marks)
15. The manager of a nationally known real estate agency has just completed a training session on appraisals for two newly hired agents. To evaluate the effectiveness of his training, the manager wishes to determine whether there is any difference in the appraised values placed on houses by these two different individuals. A sample of 12 houses is selected by the manager, and each agent is assigned the task of placing an appraised value (in thousands of dollars) on the 12 houses. The results are as follows:
HOUSE AGENT 1 AGENT 2
1 181.0 182.0
2 179.9 180.0
3 163.0 161.5
4 218.0 215.0
5 213.0 216.5
6 175.0 175.0
7 217.9 219.5
8 151.0 150.0
9 164.9 165.5
10 192.5 195.0
11 225.0 222.7
12 177.5 178.0
At the 0.05 level of significance, is there evidence of a difference in the average appraised values given by the two agents? (7 marks)
16. 1000 students at college level are graded according to their IQ and their economic conditions. Use chi square test to find out whether there is any association between economic conditions and the level of IQ.
Economic conditions IQ Level
High Medium Low Total
Rich 160 300 140 600
Poor 140 100 160 400
Total 300 400 300 1000
(7 marks)
We do not do your homework for you, especially tests. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
However, I will start you out.
1. SEm = SD/√n
2. 90% = mean ± 1.645 SEm
3. SEdiff = √(SEmean1^2 + SEmean2^2)