Assignment:
Q1 According to the Coffee Research Organization, the typical American coffee drinker consumes an average of 3.1 cups per day. A sample of 12 senior citizens revealed they consumed the following amounts, reported in cups, of coffee yesterday.
3.1, 3.3, 3.5, 2.6, 2.6, 4.3, 4.4, 3.8, 3.1, 4.1, 3.1, 3.2
At the .05 significance level does this sample data suggest there is a difference between the national average and the sample mean from senior citizens?
Q2 An investigation of the effectiveness of an antibacterial soap in reducing operating room contamination resulted in the accompanying table. The new soap was tested in a sample of eight operating rooms in the greater Seattle area during the last year.
Operating Room
A B C D E F G H
Before 6.6 6.5 9.0 10.3 11.2 8.1 6.3 11.6
After 6.8 2.4 7.4 8.5 8.1 6.1 3.4 2.0
At the 0.05 significance level, can we conclude the contamination measurements are lower after use of the new soap?
Q3 The city of Laguna Beach operates two public parking lots. The one on Ocean Drive can accommodate up to 125 cars and the one on Rio Rancho can accommodate up to 130 cars. City planners are considering both increasing the size of the lots and changing the fee structure. To begin, the Planning Office would like some information on the number of cars in the lots at various times of the day. A junior planner officer is assigned the task of visiting the two lots at random times of the day and evening and counting the number of cars in the lots. The study lasted over a period of one month. Below is the number of cars in the lots for 25 visits of the Ocean Drive lot and 28 visits of the Rio Rancho lot.
Ocean
89 115 93 79 113 77 51 75 118 105 106 91 54
63 121 53 81 115 67 53 69 95 121 88 64
Rio Rancho
128 110 81 126 82 114 93 40 94 45 84 71 74
92 66 69 100 114 113 107 62 77 80 107 90 129 105 124
Is it reasonable to conclude that there is a difference in the mean number of cars in the two lots? Use a two sample t-test to do the comparison at the .05 significance level.
Q4 The City of Maumee comprises four districts. Chief of police Andy North wants to determine whether there is a difference in the mean number of crimes committed among the four districts. He recorded the number of crimes reported in each district for a sample of six days.
Number of Crimes
Rec Center Key Street Monclova Whitehouse
13 21 12 16
15 13 14 17
14 18 15 18
15 19 13 15
14 18 12 20
15 19 15 18
At the .05 significance level, can the chief of police conclude there is a difference in the mean number of crimes? If there is a significant difference, make sure to run the Tukey test to tell which pairs of cities are different.
Q5 A research firm wants to compare the miles per gallon of unleaded regular, mid-grade, and super premium gasoline. Because of differences in the performance of different automobiles, seven different automobiles were selected and treated as blocks. Therefore, each brand of gasoline was tested with each type of automobile. The results of the trials, in miles per gallon, are shown in the following table.
Automobile Regular Mid-grade Super Premium
1 21 23 26
2 23 22 25
3 24 25 27
4 24 24 26
5 26 26 30
6 26 24 27
7 28 27 32
At the .05 significance level, is there a difference in the gasoline grades or automobiles? If there is a significant difference, make sure to run the Tukey test to tell which pairs of cities are different.
Q6 One professor teaches a large section, section A, of a particular class, and on the first test of the term, the test scores in section A were approximately normally distributed with a mean of 78 and a standard deviation of 6. Another professor also teaches a large section, section B, of the same class, and on the first test of the term, the test scores in section B were also approximately normally distributed with a mean of 74 and a standard deviation of 10.
Two students, one from each section, earned a grade of 92 on the exam. The student from section B claims that he did better because the section B test, with a mean of 74, was obviously more difficult than the section A test with a mean of 78. However, the student from section A claims that because she has a higher z-score, she actually performed "better."
Calculate the z-scores for each student's test grade and settle their dispute; that is, decide who had the superior performance on this test.
Q7 Colleges typically use grade point average cutoffs to decide who graduates with honors and who is accepted into certain programs (such as teacher education, for example). Suppose at a particular college, a GPA of 3.0 is the cutoff for such a decision. The students in department A have a grade point average of 3.77 with a standard deviation of 0.43 (for all course grades in classes taken in the department in a particular academic year).
The students in department B have a grade point average of 2.65 with a standard deviation of 1.16 for that same academic year. One student has taken most of his courses from department A; another student has taken most of her courses from department B. Both students have a GPA of 3.0.
Compare the z-scores of the two students.
Interpret what these z-scores mean.
Q8 The amount of cola in a 12-ounce can is uniformly distributed between 11.96 ounces and 12.05 ounces.
a. What is the mean amount per can?
b. What is the standard deviation amount per can?
c. What is the probability of selecting a can of cola and finding it has less than 12 ounces?
d. What is the probability of selecting a can of cola and finding it has more than 11.98 ounces?
e. What is the probability of selecting a can of cola and finding it has more than 11.00 ounces?
Q9 The net sales and the number of employees for aluminum fabricators with similar characteristics are organized into frequency distributions. Both are normally distributed. For the net sales, the mean is $180 million and the standard deviation is $25 million. For the number of employees, the mean is 1,500 and the standard deviation is 120. Clarion Fabricators had sales of $170 million and 1,850 employees.
a. Convert Clarion's sales and number of employees to z values.
b. Locate the two z values.
c. Compare Clarion's sales and number of employees with those of the other fabricators.
Q10 - Shaver Manufacturing, Inc. offers dental insurance to its employees. A recent study by the Human Resource Director shows the annual cost per employee per year followed the normal distribution, with a mean of $1,280 and a standard deviation of $420 per year.
a. What fraction of the employees cost more than $1,500 per year for dental expenses?
b. What fraction of the employees cost between $1,500 and $2,000 per year?
c. Estimate the percent that did not have any dental expense.
d. What was the cost for the 10 percent of employees who incurred the highest dental expense?