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# Statistics Question: Two-Tailed Test

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Chapter 10

For Exercises 1 & 3 answer the questions: (a) Is this a one- or two-tailed test? (b) What is the decision rule? (c) What is the value of the test statistic? (d) What is your decision regarding H0? (e) What is the p-value? Interpret it.

1. The following information is available.
H0: _ _ 50
H1: _ _ 50
The sample mean is 49, and the sample size is 36. The population standard deviation is 5.
Use the .05 significance level.

3. A sample of 36 observations is selected from a normal population. The sample mean is 21, and the sample standard deviation is 5. Conduct the following test of hypothesis using the .05 significance level.
H0: _ 20
H1: _ 20

****For Exercises 5-6: (a) State the null hypothesis and the alternate hypothesis. (b) State the decision rule. (c) Compute the value of the test statistic. (d) What is your decision regarding H0? (e) What is the p-value? Interpret it.

5. The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60,000 miles. The standard deviation of the mileage is 5,000 miles. The Crosset Truck Company bought 48 tires and found that the mean mileage for their trucks is 59,500 miles. Is Crosset's experience different from that claimed by the manufacturer at the .05 significance level?

6. The MacBurger restaurant chain claims that the waiting time of customers for service is normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The quality-assurance department found in a sample of 50 customers at the Warren Road
MacBurger that the mean waiting time was 2.75 minutes. At the .05 significance level, can we conclude that the mean waiting time is less than 3 minutes?

Chapter 11

Note: Use the five-step hypothesis testing procedure to solve the following exercises.

3. The Gibbs Baby Food Company wishes to compare the weight gain of infants using their brand versus their competitor's. A sample of 40 babies using the Gibbs products revealed a mean weight gain of 7.6 pounds in the first three months after birth. The standard deviation of the sample was 2.3 pounds. A sample of 55 babies using the competitor's brand revealed a mean increase in weight of 8.1 pounds, with a standard deviation of 2.9 pounds. At the .05 significance level, can we conclude that babies using the Gibbs brand gained less weight? Compute the p-value and interpret it.

4. As part of a study of corporate employees, the Director of Human Resources for PNC, Inc.wants to compare the distance traveled to work by employees at their office in downtown Cincinnati with the distance for those in downtown Pittsburgh. A sample of 35 Cincinnati employees showed they travel a mean of 370 miles per month, with a standard deviation of 30 miles per month. A sample of 40 Pittsburgh employees showed they travel a mean of 380 miles per month, with a standard deviation of 26 miles per month. At the .05 significance level, is there a difference in the mean number of miles traveled per month between Cincinnati and Pittsburgh employees? Use the five-step hypothesis-testing procedure.

5. A financial analyst wants to compare the turnover rates, in percent, for shares of oil-related stocks versus other stocks, such as GE and IBM. She selected 32 oil-related stocks and 49 other stocks. The mean turnover rate of oil-related stocks is 31.4 percent and the standard deviation 5.1 percent. For the other stocks, the mean rate was computed to be 34.9 percent and the standard deviation 6.7 percent. Is there a significant difference in the turnover rates of the two types of stock? Use the .01 significance level.

6. Mary Jo Fitzpatrick is the Vice President for Nursing Services at St. Luke's Memorial Hospital. Recently she noticed in the job postings for nurses that those that are unionized
seem to offer higher wages. She decided to investigate and gathered the following sample
information.
Sample
Group Mean Wage Standard Deviation Sample Size

Union \$20.75 \$2.25 40

Nonunion \$19.80 \$1.90 45

Would it be reasonable for her to conclude that union nurses earn more? Use the .02 significance level. What is the p-value?

Chapter 12

9. A real estate developer is considering investing in a shopping mall on the outskirts of
Atlanta, Georgia. Three parcels of land are being evaluated. Of particular importance is the income in the area surrounding the proposed mall. A random sample of four families is selected near each proposed mall. Following are the sample results. At the .05 significance level, can the developer conclude there is a difference in the mean income?

Use the usual five-step hypothesis testing procedure.

Southwyck Area Franklin Park Old Orchard
(\$000) (\$000) (\$000)
64 74 75
68 71 80
70 69 76
60 70 78

10. The manager of a computer software company wishes to study the number of hours senior executives spend at their desktop computers by type of industry. The manager selected a sample of five executives from each of three industries. At the .05 significance level, can she conclude there is a difference in the mean number of hours spent per week by industry?

Banking Retail Insurance
12 8 10
10 8 8
10 6 6
12 8 8
10 10 10

Chapter 13

14. Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship
between the number of client contacts and the dollar amount of sales. To document
this assertion, Mr. McWhinney gathered the following sample information. The X
column indicates the number of client contacts last month, and the Y column shows the
value of sales (\$ thousands) last month for each client sampled.

Linear Regression and Correlation
Number of Sales Number of Contacts Sales
Contacts, (\$ thousands), (\$ thousands),
X Y X Y
14 24 23 30
12 14 48 90
20 28 50 85
16 30 55 120
46 80 50 110

a. Determine the regression equation.
b. Determine the estimated sales if 40 contacts are made.

15. A recent article in Business Week listed the "Best Small Companies." We are interested in the current results of the companies' sales and earnings. A random sample of 12 companies was selected and the sales and earnings, in millions of dollars, are reported below.

Company Sales Earnings Company Sales Earnings
(\$ millions) (\$ millions) (\$ millions) (\$ millions)

Papa John's International \$89.2 4.9 Checkmate Electronics \$17.5 \$ 2.6
Applied Innovation 18.6 4.4 Royal Grip 11.9 1.7
Integracare 18.2 1.3 M-Wave 19.6 3.5
Wall Data 71.7 8.0 Serving-N-Slide 51.2 8.2
Davidson Associates 58.6 6.6 Daig 28.6 6.0
Chico's Fas 46.8 4.1 Cobra Golf 69.2 12.8

Let sales be the independent variable and earnings be the dependent variable.

a. Draw a scatter diagram.
b. Compute the coefficient of correlation.
c. Compute the coefficient of determination.
d. Interpret your findings in parts b and c.
e. Determine the regression equation.
f. For a small company with \$50.0 million in sales, estimate the earnings.

Chapter 15 Nonparametric Methods: Chi-Square Applications

6. Classic Golf, Inc. manages five courses in the Jacksonville, Florida, area. The Director
wishes to study the number of rounds of golf played per weekday at the five courses. He
gathered the following sample information.

Day Rounds
Monday 124
Tuesday 74
Wednesday 104
Thursday 98
Friday 120

At the .05 significance level, is there a difference in the number of rounds played by day of the week?

10. The chief of security for the Mall of the Dakotas was directed to study the problem of missing goods. He selected a sample of 100 boxes that had been tampered with and ascertained that for 60 of the boxes, the missing pants, shoes, and so on were attributed to
shoplifting. For 30 other boxes employees had stolen the goods, and for the remaining 10
boxes he blamed poor inventory control. In his report to the mall management, can he say
that shoplifting is twice as likely to be the cause of the loss as compared with either employee theft or poor inventory control and that employee theft and poor inventory control are equally likely? Use the .02 significance level.

Chapter 19

5. The following table lists the annual amounts of glass cullet produced by Kimble Glass
Works, Inc.
Scrap
Year Code (tons)
1999 1 2.0
2000 2 4.0
2001 3 3.0
2002 4 5.0
2003 5 6.0

Determine the least squares trend equation. Estimate the amount of scrap for the year
2005.

6. The amounts spent in vending machines in the United States, in billions of dollars, for the
years 1999 through 2003 are given below. Determine the least squares trend equation, and
estimate vending sales for 2005.
Vending Machine Sales
Year Code (\$ billions)
1999 1 17.5
2000 2 19.0
2001 3 21.0
2002 4 22.7
2003 5 24.5

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#### Solution Summary

For Exercises 1 & 3 answer the questions: (a) Is this a one- or two-tailed test? (b) What is the decision rule? (c) What is the value of the test statistic? (d) What is your decision regarding H0? (e) What is the p-value? Interpret it.

\$2.19

## Find critical value and test statistics for some t test questions

1.
Find the critical value and rejection region for the type of t-test with level of significance α and sample size n.

Right-tailed test, α = 0.1, n = 21
t0 = 2.528; t > 2.528
t0 = 1.323; t > 1.323
t0 = 1.325; t > 1.325
t0 = 1.325; t < 1.325

4.
Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.

Claim μ > 33; α = 0.005. Sample statistics: = 34, s = 3, n = 25

t0 = -2.797, standardized test statistic ≈ -1.667, fail to reject H0; There is not sufficient evidence to support the claim
t0 = 2.797, standardized test statistic ≈ 1.667, reject H0; There is sufficient evidence to reject the claim
t0 = 2.797, standardized test statistic ≈ 1.667, fail to reject H0; There is not sufficient evidence to support the claim
5.
Find the critical value and rejection region for the type of t-test with level of significance α and sample size n.
Left-tailed test, α = 0.1, n = 22
t0 = -2.518; t < -2.518
t0 = -1.321; t < -1.321
t0 = 1.323; t > 1.323
t0 = -1.323; t < -1.323

6.
Find the critical value and rejection region for the type of t-test with level of significance α and sample size n.
Two-tailed test, α = 0.1, n = 23
t0 = -1.717, t0 = 1.717; t < -1.717, t > 1.717
t0 = -1.321, t0 = 1.321; t < -1.321, t > 1.321
t0 = -1.714, t0 = 1.714; t < -1.714, t > 1.714
t0 = 1.717; t > 1.717
7.
Find the standardized test statistic t for a sample with n = 10, = 16.5, s = 1.3, and if Round your answer to three decimal places.
-3.010
-2.189
-3.186
-2.617
8.
Find the standardized test statistic t for a sample with n = 12, = 21.7, s = 2.1, and if Round your answer to three decimal places.
-0.008
-0.825
-0.037
-0.381
9.
Find the standardized test statistic t for a sample with n = 12, = 31.2, s = 2.2, and α = 0.01 if Round your answer to three decimal places.
1.890
2.132
2.001
1.991

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