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BIA 2610 Statistics –Final Exam (Sample Questions)

Scott Bell Builders would like to predict the total number of labor hours spent framing a house based on

the square footage of the house. The following data has been compiled on ten houses recently built.

Square

Footage

(100s)

Framing

Labor

Hours

Square

Footage

(100s)

Framing

Labor

Hours

20 195 27 225

21 170 29 240

23 220 31 225

23 200 32 275

26 230 35 260

Use the output from Excel's Regression Tool in finding answers to the items below the output.

Regression Statistics

Multiple R 0.920

R Square 0.846

Adjusted R Square 0.827

Standard Error 10.997

Observations 10

ANOVA

df SS MS F Significance F

Regression 1 5322.46351 5322.46351 44.008 0.00016

Residual 8 967.53649 120.94206

Total 9 6290

Coefficients Standard Error t Stat P-value

Intercept 94.456 19.83489 4.762 0.00142

Sq Footage (100s) 4.852 0.73137 6.634 0.00016

a. Develop the least-squares estimated regression equation that relates framing labor hours to house

square footage. (5 pts.)

b. Use the regression equation developed in part (a) to predict framing labor hours (to the nearest hour)

when the house size is 3350 square feet. (5 pts.)

c. At the .01 level of significance, is there sufficient evidence that a linear relationship exists between

framing labor hours and house square footage? (5 pts.)

d. What percentage of the variation in framing labor hours may be attributed to the linear relationship

between framing labor hours and house square footage? (to the nearest tenth of a percent) ( 5 pts.)

e. What is the value of the sample correlation coefficient? (to two decimal places) ( 5 pts.)

For a sample of 20 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000

residents) as a function of its median income (in $1,000s). A portion of the regression results are as follows.

ANOVA df SS MS F Significance F

Regression

6,213.18

Residual

92,509.61

Total

98,722.79

Coefficients Standard Error t Stat p-value Lower 95% Upper 95%

Intercept 848.9971 114.0838 7.4419 0.0000 608.28 1,089.71

Income 3.4245 14.6793 0.2333 0.8183 −27.55 34.40

a. Specify the estimated regression equation.

b. Choose the appropriate hypotheses to test whether the Income and the crime rate are linearly related.

H0: β1 = 0; HA: β1 ≠ 0

H0: β1 ≤ 0; HA: β1 > 0

H0: β1 ≥ 0; HA: β1 < 0

c. At the 5% significance level, what is the conclusion to the hypothesis test? Why?

Reject H0 the income and the crime rate are not linearly related.

Do not reject H0 the income and the crime rate are not linearly related.

Reject H0 the income and the crime rate are linearly related.

Do not reject H0 the income and the crime rate are linearly related.

d. What is 95% confidence interval for the slope coefficient of Income.

Confidence interval to

e. Using the p-value approach, determine whether income is significant in explaining the crime rate at the 5%

significance level. Why?

Income is not significant in explaining the crime rate, since its slope coefficient does not significantly

differ from zero.

Income is significant in explaining the crime rate, since its slope coefficient significantly differs from

zero.

Income is not significant in explaining the crime rate, since its slope coefficient significantly differs

from zero.

Income is significant in explaining the crime rate, since its slope coefficient does not significantly

differ from zero.

2.

t-Test: Sample

Process A Assembly Time

(minutes)

Process A Assembly Time

(minutes)

6.8

5.0 Mean 6.288

7.9 Variance 0.847766667

5.2 Observations 25

7.6 Pooled Variance 1.075416667 5.0 5.9 df 48 5.2 t Stat 0.927332603 6.5 P(T<=t) one-tail 0.179196744 7.4 t Critical one-tail 1.677224197 6.1 P(T<=t) two-tail 0.358393488 6.2 t Critical two-tail 2.010634722

7.1 4.6 6.0 7.1 6.1 5.0 6.3 7.0 6.4 6.1 6.6 7.7 6.4

3. There is one Processes A to assemble an auto part. Is it true that Process A takes significantly more

time then 6 minutes? Above are the results for Significance level (alpha = 0.05)

a. State null and alternative hypothesis.

b. Draw the normal distribution and shade the rejection area.

c. What is the critical statistics?

d. What is computed statistics?

e. Show computed and critical statistics on the normal distribution.

f. Justify your acceptance/rejection of null/alternative hypothesis.

g. What is the p-value? Justify your acceptance/rejection of null/alternative hypothesis according to p-

value approach.

21. From a population of cans of coffee marked "12 ounces," a sample of 25 cans is selected and the

contents of each can are weighed. The sample revealed a mean of 11.84 ounces and a standard deviation

of 0.5 ounces. Assume the population is normally distributed. At the .05 level of significance we are

looking for sufficient evidence to conclude that, on average, the customers are receiving less than 12

ounces per can.

a. What is the appropriate test statistic formula? ( 5 pts.)

b. Assuming that the appropriate test statistic is Z and the computed value is -1.58, what is the p-value? (

5 pts.)

c. Assuming that the appropriate test statistic is t and the computed value is -1.58, what is (are) the critical

value(s)? ( 5 pts.)

d. Assuming that the appropriate test statistic is Z, the computed value is -1.58, and the critical value is -

1.645, may we conclude that the customers are being "shorted?" (Yes or No) ( 5 pts.)

22. A lathe is set to cut bars of steel into lengths of 6 centimeters. The lathe is considered to be in perfect

adjustment if the average length of the bars it cuts is 6 centimeters. A sample of 121 bars is selected

randomly and measured. It is determined that the average length of the bars in the sample is 6.068

centimeters. The population standard deviation is 0.44 centimeters. Determine whether or not we can

prove the lathe is not in perfect adjustment. Use a .05 level of significance.

a. What is the appropriate test statistic formula? ( 5 pts.)

b. Assuming that the appropriate test statistic is Z and the computed value is 1.70, what is the p-value? ( 5

pts.)

c. Assuming that the appropriate test statistic is t and the computed value is 1.70, what is (are) the critical

value(s)? ( 5 pts.)

d. Assuming that the appropriate test statistic is Z, the computed value is 1.70, and the critical values are

1.96, may we conclude that the lathe is not in perfect adjustment? (Yes or No) ( 5 pts.)

23. A new soft drink is being market tested. If the company can find evidence that more than 20% of their

customers like the taste, they plan to market it. A sample of 400 individuals participated in the taste test

and 98 indicated they like the taste. At the .03 level of significance, do the sample results give them

sufficient evidence to market the new soft drink?

a. What is the appropriate test statistic formula? ( 5 pts.)

b. What is (are) the critical value(s) of the hypothesis test? ( 5 pts.)

c. What is the computed value of the test statistic? ( 5 pts.)

d. If the p-value is 0.0122, should the company market the new soft drink? (Yes or No) ( 5 pts.)

24. Zip, Inc. manufactures Zip drives on two different manufacturing processes. Because the management

of this company is interested in determining if process 1 takes less manufacturing time, they selected

independent samples from each process. The results of the samples are shown below. Use Process 1 as

population 1 and process 2 as population 2 in responding to all problems and conduct the hypothesis test

at the 0.01 level of significance.

Process 1 Process 2

Sample Size 27 22

Sample Mean (in minutes) 10 14

Sample Variance 16 25

a. State the null and alternative hypotheses. ( 5 pts.)

b. Assuming there are 39 degrees of freedom for the t test, what is (are) the critical value(s)? ( 5pts.)

c. What is the computed value of the test statistic? (to three decimal places) ( 5 pts.)

d. Based upon your answers in b. and c., is there is sufficient evidence to indicate that process 1 takes a

significantly shorter time to manufacture the Zip drives? (5 pts.)

25. Maxforce, Inc., manufactures racquetball racquets by two different manufacturing processes (A and

B). Because the management of this company is interested in estimating the difference between the

average time it takes each process to produce a racquet, they select independent samples from each

process. The results of the samples are shown below. Use Process A as population 1 and Process B as

population 2 in your response.

Process A Process B

Sample Size 32 35

Sample Mean (in minutes) 43 47

Population Variance (σ 2 )

64 70

Develop a 95% confidence interval estimate for the difference between the average time of the two

processes. Show your work and then explain whether or not the result shows evidence of a significant

difference. (10 pts.)

3. The governor of our state believes that average income of state employees is less than

$40,000. The population standard deviation is $10,000. A sample of 100 employees resulted in

mean salary of $39,000.

Show all work including Distribution, rejection area, critical and test statistics.

a. State the appropriate null and alternative hypothesis regarding Governor’s belief regarding average income.

b. Using a significance level of 2%, what is the critical value of Z?

c. What is the Z Statistics?

Show where it falls in the distribution drawn in part b.

d. Is Governor’s belief acceptable or unacceptable?

Explain your answer in terms of part b and part c.