True / False Questions
1. The further the hypothesized mean is from the actual mean the lower is the power of the test.
2. 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. She knows the population standard deviation and 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 .047 for the test. If the significance level is .05, the null hypothesis would be rejected. Assume that the population of pressure values is normally distributed.
3. The larger the p-value, the more we doubt the null hypothesis.
4. You cannot make a Type I error when the null hypothesis is true.
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 increase the probability of a Type I error.
6. When conducting a hypothesis test about a single mean, other relevant factors held constant, increasing the level of significance from .05 to .10 will reduce the probability of a Type II error.
7. When the null hypothesis is false, you can make Type II error.
8. The error term is the difference between the actual value of the dependent variable and the corresponding mean value of the dependent variable.
9. The Coefficient of Determination shows the direction of relationship between the dependent and the independent variables.
10. The coefficient of determination is the proportion of total variation explained by the regression line.
11. The intercept of the simple linear regression equation represents the average change in the value of the dependent variable per unit change in the independent variable (X).
12. The correlation coefficient is the ratio of explained variation to total variation.
13. Even if there is a strong correlation between the independent and dependent variable, we may not expect that an increase in the value of the independent variable is associated with an increase in the value of the dependent variable.
Multiple Choice Questions
1. Which statement is incorrect?
A. The null hypothesis contains the equality sign
B. When a false null hypothesis is not rejected, a Type II error has occurred
C. If the null hypothesis is rejected, it is concluded that the alternative hypothesis is true
D. If we reject the null hypothesis, we cannot commit Type I error
2. For a given hypothesis test, if we do not reject H0 and H0 is true.
A. No error has been committed
B. Type I error has been committed
C. Type II error has been committed
D. The model is weak
3. If a null hypothesis is rejected at a significance level of 0.05, it will ______ be rejected at a significance level of 0.10
A. Always
B. Sometimes
C. Never
4. If a null hypothesis is not rejected at a significance level of .05, it will ______ be rejected at a significance level of .01
A. Always
B. Sometimes
C. Never
5. If a one-sided null hypothesis is rejected for a single mean at a given significance level, the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation and the same mean) will _________ be rejected at the same significance level.
A. Always
B. Sometimes
C. Never
6. A professional basketball player is averaging 21 points per game. He will be retiring at the end of this season. The team has multiple options to replace him. However, the owner feels that signing a replacement is only justified, if he can average at least 22 points per game. Which of the following are the appropriate hypotheses for this problem?
A. H0: m £ 21 vs. Ha: m > 21
B. H0: m £ 22 vs. Ha: m > 22
C. H0: m ³ 21 vs. Ha: m < 21
D. H0:m ³ 22 vs. Ha: m < 22
7. When carrying out a large sample test of H0: m £ 10 vs. Ha: m > 10 by using a critical value approach, we reject H0 at level of significance a when the calculated test statistic is:
A. Less than za
B. Less than - za
C. Greater than za
D. Greater than za/2
E. Less than the p value
8. If you live in California, the decision to buy earthquake insurance is an important one. A survey revealed that only 133 of 337 randomly selected residences in one California county were protected by earthquake insurance. Calculate the appropriate test statistic to test the hypothesis which leads to the alternate hypothesis that less than 40% of the residents are protected by earthquake insurance?
A.- 0.20
B. 0.40
C. -0.13
D. 0.20
E. -0.40
9. In a simple linear regression analysis, the correlation coefficient (a) and the slope (b) _____ have the same sign.
A. Always
B. Sometimes
C. Never
10. The least squares regression line minimizes the sum of the
A. Differences between actual and predicted Y values
B. Squared differences between actual and predicted Y values
C. Absolute deviations between actual and predicted X values
D. Absolute deviations between actual and predicted Y values
E. Squared differences between actual and predicted X values
11. The ___________ the R2 and the __________ the s (standard error), the stronger the relationship between the dependent variable and the independent variable.
A. Higher, lower
B. Lower, higher
C. Lower, lower
D. Higher, higher
12. In simple regression analysis the quantity that gives the amount by which Y (dependent variable) changes for a unit change in X (independent variable) is called the
A. Coefficient of determination
B. Standard error
C. The Y intercept of the regression line
D. Correlation coefficient
E. Slope of the regression line
13. The correlation coefficient may assume any value between
A. 0 and 1
B. -1 and 1
C. -infinity and + infinity
D. 0 and infinity
E. -1 and 0
14. In simple regression analysis, if the correlation coefficient is a positive value, then
A. The Y intercept must also be a positive value
B. The coefficient of determination can be either positive or negative, depending on the value of the slope
C. The least squares regression equation could either have a positive or a negative slope
D. The slope of the regression line must also be positive
E. The standard error of estimate can either have a positive or a negative value
Essay Questions
1. Test H0: m £ 8 versus HA: m > 8, given a = 0.01, n = 25, = 8.13 and s = 0.25. Assume the sample is selected from a normally distributed population.
2. Test H0: π = 0.2 versus HA: π ¹ 0.2 with p = 0.3 and n = 100 at alpha = 0.05 and 0.01.
3. Test at α = 0.01 the hypothesis that a majority (more than 50%) of students favor the plus/minus grading system at a university if in a random sample of 500 students, 275 favor the system?
4. Test whether the sample evidence indicates that the average time an employee stays with a company in their current positions is less than 3 years when a random sample of 64 employees yielded a mean of 2.76 years and s = 0.8. Use a = 0.01. Assume normal distribution.
5. Use the following results obtained from a simple linear regression analysis with 15 observations.
= 35.5- (1.25)X
R2= 0.8745 and sb1 = 0.50
Interpret regression results and the value of the coefficient of Determination. Predict the value of Y when X is equal to 10. Calculate the correlation coefficient between Y and X. Test to determine if there is a significant relationship between the independent and dependent variable at a = 0.05. Perform a two-tailed test.
6. An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 20 metal sheets are given below. Use the simple linear regression model.
∑X = 40
∑X2 = 200
∑Y = 70
∑Y2 = 545
∑XY = 320
Find the estimated y intercept and slope and write the equation of the least squares regression line. Estimate Y when X is equal to 3 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation.