Exercise for final exam - Statistics for Business | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố HCM

Vietnam International University (VNU) H – CMC
Semester 02, Academic Year 2015 - 2016
INTERNATIONAL UNIVERSITY (IU) ------o0o------ REVIEW MATERIAL ------o0o------
CHAPTER 07: HYPOTHESIS TESTING Question 1:
When a certain production process is operating properly, it produces items that each has a measurable
characteristic with mean 122 and standard deviation 9. However, occasionally the process goes out of
control, which results in a change in the mean of the items produced. Given a random sample of 10
recently produced items had the following values: 123 120 115 125 131 127 130 118 125 128
a. Is the production process operating properly? Conduct the appropriate test of hypothesis and draw the
conclusion at a 10% significance level.
b. Calculate 95% confidence interval of population parameter given in this question. Question 2:
When a certain production process is operating properly, it produces items that each has a measurable
characteristic with mean 122. However, occasionally the process goes out of control, which results in the
increase in the mean of the items produced. Given a random sample of 10 recently produced items had the following values: 123 120 115 125 131 127 130 118 125 128
a. Is the production of process out of control? Conduct the appropriate test of hypothesis and draw the
conclusion at a 5% significance level.
b. Calculate the 90% confidence interval of the population parameter given in this question. Question 3:
It is extremely important in a certain chemical process that a solution to be used as a reactant has a pH
level greater than 8.40. It is a very serious mistake to run the process with a reactant having a pH level
less than or equal to 8.40. The scientists want to test whether the certain process has any serious mistake
given a sample of 30 independent measurements yielded the following pH values: 8.30 8.42 8.44 8.32 8.43 8.41 8.42 8.46 8.37 8.42 8.39 8.47 8.42 8.37 8.45 8.45 8.34 8.48 8.36 8.35 8.37 8.42 8.46 8.32 8.38 8.46 8.30 8.39 8.45 8.37
a. Conduct the appropriate test of hypothesis and draw the conclusion at a 1% significance level.
b. Calculate the 98% confidence interval of the population parameter given in this question. Page of 1 5
Course: Statistics for Business (BA080IU) | Group 01 | Lecturer: Dr. Phan Nguyen Ky Phuc Paper Title: REVIEW MATERIAL
Vietnam International University (VNU) H – CMC
Semester 02, Academic Year 2015 - 2016
INTERNATIONAL UNIVERSITY (IU) ------o0o------ Question 4:
According to a survey of 2000 women aged 16 years and over (Census Bureau, 2010), there were 1539
women driving alone to work. To examine whether the percentage of women driving alone to work
changes after 4 years, a recent survey of 2256 women shows that there are 1934 of them drive alone to work.
a. Conduct the appropriate test of hypothesis and draw the conclusion at a 10% significance level.
b. Calculate the 90% confidence interval for the population parameter given in this question.
CHAPTER 08: COMPARISON OF TWO POPULATIONS Question 1:
A sample of 16 packs of Brand A nutritious cereal gave the mean number of calories of 25 per pack with
a standard deviation of 4 calories. Another sample of 18 packs of Brand B nutritious cereal gave the
mean number of calories of 27 per pack with a standard deviation of 5 calories. Is there any difference in
the mean number of calories between these two brands of nutritious cereal? Assume that the calories per
pack of nutritious cereal are normally distributed for each of the two brands and that the standard
deviations for the two populations are equal.
a. Conduct the appropriate test for hypothesis and draw the conclusion at a 1% significance level.
b. Calculate the 90% confidence interval for the difference in mean values between two given populations. Question 2:
A sample of 16 packs of Brand A nutritious cereal gave the mean number of calories of 25 per pack with
a standard deviation of 4 calories. Another sample of 18 packs of Brand B nutritious cereal gave the
mean number of calories of 27 per pack with a standard deviation of 5 calories. Is there any difference in
the mean number of calories between these two brands of nutritious cereal? Assume that the calories per
pack of nutritious cereal are normally distributed for each of the two brands and that the standard
deviations for the two populations are unequal.
a. Conduct the appropriate test for hypothesis and draw the conclusion at a 1% significance level.
b. Calculate the 90% confidence interval for the difference in mean values between two given populations. Question 3:
In an experiment on braking performance, two tire manufacturers: ABC and XYZ measured the
stopping distance for their tire models on dry pavement. On a test track, cars made repeated stops from
60 miles per hour, with results shown in the following table: Test track 1 2 3 4 5 6 7 8 9 10 Stopping Company ABC 145 152 141 143 131 148 126 140 135 133
Distance (ft.) Company XYZ 150 147 136 134 130 134 134 128 136 158 Page of 2 5
Course: Statistics for Business (BA080IU) | Group 01 | Lecturer: Dr. Phan Nguyen Ky Phuc Paper Title: REVIEW MATERIAL
Vietnam International University (VNU) H – CMC
Semester 02, Academic Year 2015 - 2016
INTERNATIONAL UNIVERSITY (IU) ------o0o------
Is there any difference in the average stopping distance between two tire manufacturers? If yes, which
tire manufacturer has better braking performance?
Case 1: Assuming that the samples of stopping distance are paired samples.
a. Conduct the appropriate test for hypothesis and draw the conclusion at a 1% significance level.
b. Calculate the 95% confidence interval for the difference between population parameters given in this question.
Case 2: Assuming that the samples of stopping distance are independent random samples.
a. Given equal population variances, conduct the appropriate test for hypothesis and draw the conclusion
at a 1% significance level. Calculate the 95% confidence interval for the difference between population
parameters given in this question.
b. Given the unequal population variances, conduct the appropriate test for hypothesis and draw the
conclusion at a 1% significance level. Calculate the 95% confidence interval for the difference between
population parameters given in this question.
c. Test the validity of the equal variance assumption for the data presented in this question. Question 4:
A pharmaceutical company launching a new type of capsule for the obese claime d that “the use of diet
capsule assists the obese in losing at least 2 kilograms in the first week compared to the obese denying
the use of this”. The weights of 10 voluntary persons before and after trying this diet capsule are given
in the following table. Volunteer 1 2 3 4 5 6 7 8 9 10 Weight Before 89 95 84 103 98 93 115 88 96 101 (kg) After 86 96 82 97 98 88 112 87 92 95
Did the pharmaceutical company exaggerate the effect of the diet capsule?
a. Conduct the appropriate test of hypothesis and draw the conclusion at a 2.5% significance level.
b. Calculate the 95% confidence interval for the difference between population parameters given in this question. Question 5:
A chef is considering giving extra flavor to the sauce by adding tomatoes or cheese to improve his
dishes. To determine the customers’ taste, the chef randomly selects 15 customers and asks them to try
and score these two flavors of sauce. The following table gives the scores (on a scale from 0 to 100) on
each new flavor of sauce for each of these 15 customers. Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Tomato 90 73 75 89 86 79 86 81 75 77 82 75 70 89 72 Flavor
Cheese 77 89 74 79 90 81 74 83 70 79 71 89 85 76 79
Is there any difference in the customer preference for new flavor of sauce? Which flavor of sauce do they prefer? Page of 3 5
Course: Statistics for Business (BA080IU) | Group 01 | Lecturer: Dr. Phan Nguyen Ky Phuc Paper Title: REVIEW MATERIAL
Vietnam International University (VNU) H – CMC
Semester 02, Academic Year 2015 - 2016
INTERNATIONAL UNIVERSITY (IU) ------o0o------
a. Conduct the appropriate test for hypothesis and draw the conclusion at 10% significance level.
b. Calculate the 98% confidence interval for the difference between population parameters given in this question. Question 6:
In the last presidential election, the difference between the percentage of male registered voters and the
percentage of female registered voters (%male - %female) is 2. A statistical test is performed to examine
whether the difference between the percentage of male and female registered voters stays the same in the
latest election. Based on recent the survey, there are 285 out of 500 males and 218 out of 400 females registering to vote.
a. Conduct the appropriate test for hypothesis and draw the conclusion at 1% significance level.
b. Calculate the 99% confidence interval for the difference between population parameters given in this question. Question 7:
On a standardized test of students in two classes A and B, there are 71 out of 100 students from class A
and 81 out of 110 students from class B achieving “over 70” GPA. Is the percent of students having their
GPAs greater than 70 different between two classes?
a. Conduct the appropriate test for hypothesis and draw the conclusion at 1% significance level.
b. Calculate the 90% confidence interval for the difference between population parameters given in this question.
CHAPTER 09: ANALYSIS OF VARIANCE (ANOVA) Question:
Recently, four new brands of nylon rope launched by company ABC are advertised as having a breaking
strength of 100 pounds. To guarantee the breaking strengths of the four brands are equally qualified,
researchers have obtained and tested these samples, with results shown in the following table: Test record 1 2 3 4 5 6 Brand A 103.1 108.9 106.7 114.3 113.3 110.5 Breaking Strengths Brand B 111.6 117.8 109.8 110.1 118.3 116.7 (lbs.) Brand C 109.0 111.8 113.0 109.7 108.6 114.7 Brand D 118.0 115.8 114.2 117.3 113.8 110.6
Given the ANOVA table, conduct the appropriate test for hypothesis and draw the conclusion at a 5% significance level. ANOVA Table Source of Variation SS df MS F-ratio Treatment 38.8678 Page of 4 5
Course: Statistics for Business (BA080IU) | Group 01 | Lecturer: Dr. Phan Nguyen Ky Phuc Paper Title: REVIEW MATERIAL
Vietnam International University (VNU) H – CMC
Semester 02, Academic Year 2015 - 2016
INTERNATIONAL UNIVERSITY (IU) ------o0o------ Error Total 349.08
CHAPTER 11: MULTIPLE REGRESSION Question:
A placement director of a university thought that the grade point average (GPA) and the number of
university activities listed on the résumé might have effect on the starting salaries of the graduates. In
recent analysis, the data output is shown in the following tables: Table 1 SS df MS F-ratio Regression Error 2.731 Total 83.6 9 Table 2 Coefficients Standard Error t Stat p-value Intercept 23.6078 3.6847 GPA 4.5367 1.3387 Number of activities 1.2438 0.5027
a. Do the grade point average (GPA) and the number of university activities listed on the résumé have
effect on the starting salaries of the graduates? Conduct the F test and draw the conclusion at a 5% significance level.
b. Specify the model expressing the estimated regression relationship of starting salaries on the grade
point average (GPA) and the number of university activities.
c. Do the variables of the grade point average (GPA) and the number of university activities have the
explanatory power with respect to the variable of starting salaries of the graduates? Conduct the test of
significance of individual regression parameters and draw the conclusion at a 5% significance level. -----THE END---- - Page of 5 5
Course: Statistics for Business (BA080IU) | Group 01 | Lecturer: Dr. Phan Nguyen Ky Phuc Paper Title: REVIEW MATERIAL