Bus 578 Business Statistics
A complete assignment covering statistical methods and business analytics.
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Assignment 3
Business Statistics
Bus 578
Spring- 2014
Ahmed Hossain
CWID: 50116869
Date: 4/6/2014
Assignment-3 (Chs. 9, 10 and 12)
Due by Midnight of Sunday, April 6th, 2014: Total 75 points
True/False (One point each)
Chapter 9
1. The manager of the quality department for a tire manufacturing company wants to know the
average tensile strength of rubber used in making a certain brand of radial tire. The population is
normally distributed and the population standard deviation is known. She uses a Z test to test the
null hypothesis that the mean tensile strength is 800 pounds per square inch. The calculated Z
test statistic is a positive value that leads to a p-value of .009 for the test. If the significance level
() is .01, the null hypothesis would be rejected. True
2. You cannot make a Type II error when the null hypothesis is true. True
Assignment 3
Business Statistics
Bus 578
Spring- 2014
Ahmed Hossain
CWID: 50116869
Date: 4/6/2014
Assignment-3 (Chs. 9, 10 and 12)
Due by Midnight of Sunday, April 6th, 2014: Total 75 points
True/False (One point each)
Chapter 9
1. The manager of the quality department for a tire manufacturing company wants to know the
average tensile strength of rubber used in making a certain brand of radial tire. The population is
normally distributed and the population standard deviation is known. She uses a Z test to test the
null hypothesis that the mean tensile strength is 800 pounds per square inch. The calculated Z
test statistic is a positive value that leads to a p-value of .009 for the test. If the significance level
() is .01, the null hypothesis would be rejected. True
2. You cannot make a Type II error when the null hypothesis is true. True
2
3. The power of a statistical test is the probability of not rejecting the null hypothesis when it is
true. False
4. The level of significance indicates the probability of rejecting a false null hypothesis. False
5. When conducting a hypothesis test about a single mean, other relevant factors held constant,
increasing the level of significance from .05 to .10 will decrease the probability of a Type II
error. True
Chapter10
6. In an experiment involving matched pairs, a sample of 14 pairs of observations is collected.
The degree of freedom for the t statistic is 12. False
7. In testing the difference between two means from two independent populations, the sample
sizes do not have to be equal to be able to use the Z statistic. True
8. In testing the difference between the means of two independent populations, if neither
population is normally distributed, then the sampling distribution of the difference in means will
be approximately normal provided that the sum of the sample sizes obtained from the two
populations is at least 30. True
9. If the limits of the confidence interval of the difference between the means of two normally
distributed populations were 0.5 and 2.5 at the 95% confidence level, then we can conclude that
we are 95% certain that there is no significant difference between the two population means.
False
10. When comparing two population means based on independent random samples, the pooled
estimate of the variance is used if the population standard deviations are not known and assumed
unequal. False
Chapter 12
11. The chi-square distribution is a continuous probability distribution that is always skewed to
the right. True
12. In a contingency table, when all the expected frequencies equal the observed frequencies the
calculated
2 statistic equals 1. False
13. In a contingency table, if all of the expected frequencies equal the observed frequencies, then
we can conclude that there is a perfect dependence between rows and columns. False
14. In performing a chi-square test of independence, as the difference between the respective
observed and expected frequencies decrease, the probability of concluding that the row variable
is independent of the column variable increases. True
3. The power of a statistical test is the probability of not rejecting the null hypothesis when it is
true. False
4. The level of significance indicates the probability of rejecting a false null hypothesis. False
5. When conducting a hypothesis test about a single mean, other relevant factors held constant,
increasing the level of significance from .05 to .10 will decrease the probability of a Type II
error. True
Chapter10
6. In an experiment involving matched pairs, a sample of 14 pairs of observations is collected.
The degree of freedom for the t statistic is 12. False
7. In testing the difference between two means from two independent populations, the sample
sizes do not have to be equal to be able to use the Z statistic. True
8. In testing the difference between the means of two independent populations, if neither
population is normally distributed, then the sampling distribution of the difference in means will
be approximately normal provided that the sum of the sample sizes obtained from the two
populations is at least 30. True
9. If the limits of the confidence interval of the difference between the means of two normally
distributed populations were 0.5 and 2.5 at the 95% confidence level, then we can conclude that
we are 95% certain that there is no significant difference between the two population means.
False
10. When comparing two population means based on independent random samples, the pooled
estimate of the variance is used if the population standard deviations are not known and assumed
unequal. False
Chapter 12
11. The chi-square distribution is a continuous probability distribution that is always skewed to
the right. True
12. In a contingency table, when all the expected frequencies equal the observed frequencies the
calculated
2 statistic equals 1. False
13. In a contingency table, if all of the expected frequencies equal the observed frequencies, then
we can conclude that there is a perfect dependence between rows and columns. False
14. In performing a chi-square test of independence, as the difference between the respective
observed and expected frequencies decrease, the probability of concluding that the row variable
is independent of the column variable increases. True
3
15. When we carry out a chi-square test of independence, the expected frequencies are based on
the Null hypothesis. True
Multiple Choices (Two points each)
Chapter 9
1. If a null hypothesis is rejected at a significance level of .05, it will ______ be rejected at a
significance level of .01
A. Always
B. Sometimes
C. Never
2. If a null hypothesis is not rejected at a significance level of .10, it will ______ be rejected at a
significance level of .05
A. Always
B. Sometimes
C. Never
3. When carrying out a large sample test of H0:
=10 vs. Ha:
10 by using a p-value, we
reject H0 at level of significance
when the p-value is:
A. Greater than
/2
B. Greater than
C. Less than
D. Less than
/2
E. Less than Z
4. If you live in California, the decision to buy earthquake insurance is an important one. A
survey revealed that only 119 of 340 randomly selected residences in one California County
were protected by earthquake insurance.
Calculate the appropriate test statistic to test the hypotheses that 40% or more buy the insurance.
(You are dealing with proportions which are small numbers. Therefore keep at least four decimal
places in your intermediate steps and do the rounding to the two decimal places at the end only).
A. 1.88
B. 1.93
C. -1.88
D. -1.93
E. -1.65
Chapter 10
5. In order to test the effectiveness of a drug called XZR designed to reduce cholesterol levels,
20 heart patients' cholesterol levels are measured before they are given the drug. The same 20
15. When we carry out a chi-square test of independence, the expected frequencies are based on
the Null hypothesis. True
Multiple Choices (Two points each)
Chapter 9
1. If a null hypothesis is rejected at a significance level of .05, it will ______ be rejected at a
significance level of .01
A. Always
B. Sometimes
C. Never
2. If a null hypothesis is not rejected at a significance level of .10, it will ______ be rejected at a
significance level of .05
A. Always
B. Sometimes
C. Never
3. When carrying out a large sample test of H0:
=10 vs. Ha:
10 by using a p-value, we
reject H0 at level of significance
when the p-value is:
A. Greater than
/2
B. Greater than
C. Less than
D. Less than
/2
E. Less than Z
4. If you live in California, the decision to buy earthquake insurance is an important one. A
survey revealed that only 119 of 340 randomly selected residences in one California County
were protected by earthquake insurance.
Calculate the appropriate test statistic to test the hypotheses that 40% or more buy the insurance.
(You are dealing with proportions which are small numbers. Therefore keep at least four decimal
places in your intermediate steps and do the rounding to the two decimal places at the end only).
A. 1.88
B. 1.93
C. -1.88
D. -1.93
E. -1.65
Chapter 10
5. In order to test the effectiveness of a drug called XZR designed to reduce cholesterol levels,
20 heart patients' cholesterol levels are measured before they are given the drug. The same 20
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Document Details
University
Baldwin Wallace University
Subject
Statistics