Question 1. The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a week, end is $600 or less. A member of the hotel's accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of future weekend guest bills to test the manager's claim.
a. Which form of the hypotheses should be used to test the manager's claim? Explain,
H0: μ ≥ 600 H0: μ ≤ 600 H0: μ = 600
H0: p. < 600 Ha: μ > 600 Ha: μ ≠ 600
b. What conclusion is appropriate when He cannot be rejected?
c. What conclusion is appropriate when He can be rejected?
Question 2. Carpetland salespersons average $8000 per week in sales. Steve Contois, the firm's vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson.
a. Develop the appropriate null and alternative hypotheses.
b. What is the Type I error in this situation? What are the consequences of making this error?
c. What is the Type II error in this situation? What are the consequences of making this error?
Question 3: Speaking to a group of analysts in January 2006, a brokerage firm executive claimed that at least 70% of investors are currently confident of meeting their investment objectives. A UBS Investor Optimism Survey, conducted over the period January 2 to January 15, found that 67% of investors were confident of meeting their investment objectives (CNBC, January 20, 2006).
a. Formulate the hypotheses that can be used to test the validity of the brokerage firm executive's claim.
b. Assume the UBS Investor Optimism Survey collected information from 300 investors. What is the p-value for the hypothesis test?
c. At α = .05, should the executive's claim be rejected?
Question 4:
The data from exercise 1 follow.
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xi
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1
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2
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3
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4
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5
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yi
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3
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7
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5
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11
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14
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The estimated regression equation for these data is jr = .20 + 2.60x.
a. Compute SSE, SST, and SSR using equations (14.8), (14.9), and (14.10).
b. Compute the coefficient of determination r2. Comment on the goodness of fit.
c. Compute the sample correlation coefficient.
Question 5:
The data from exercise 2 follow.
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xi
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3
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12
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6
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20
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14
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yi
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1 55
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40
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55
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10
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15
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a. Compute an estimate of the standard deviation of y^* when x = 8.
b. Develop a 95% confidence interval for the expected value of y when x = 8.
c. Estimate the standard deviation of an individual value of y when x = 8.
d. Develop a 95% prediction interval for y when x = 8.
Question 6:
Following is a portion of the Excel output for a regression analysis relating maintenance expense (dollars per month) to usage (hours per week) for a particular brand of computer terminal.
ANOVA
df SS
Regression 1 1575.76
Residual 8 349.14
Total 9 1924.90
Coefficients Standard Error t Stat
Intercept 6.1092 .9361
Usage 0.8951 .149
a. Write the estimated regression equation.
b. Use a t test to determine whether monthly maintenance expense is related to usage at the .05 level of significance.
c. Did the estimated regression equation provide a good fit? Explain.
Question 7:
Consider the following data for two variables, x and y.
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xi
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4
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5
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7
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8
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10
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12
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12
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22
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yi
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12
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14
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16
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15
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18
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20
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24
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19
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a. Develop a scatter diagram for these data. Does the scatter diagram indicate any influential observations? Explain.
b. Compute the standardized residuals for these data. Do the data include any outliers? Explain.
c. Compute the leverage values for these data. Do there appear to be any influential observations in these data? Explain.