## [answered] BUSM225 1. The manager of a local store believes that the s

BUSM225

1. The manager of a local store believes that the store?s average daily sales are more than \$8,000. To

test her belief, a sample of 64 days of sales was selected; and it was found that the average daily

sale was \$8,250 with a standard deviation (of the sample ) of \$1,200.

a. Perform a hypothesis test of the manager?s belief at the 5% level of significance.

b. What is the p-value of this test and state its meaning. 2. From a population of cereal boxes marked ?12 ounces?, a sample of 16 boxes is selected and the

contents of each box is weighed. The sample revealed a mean of 11.7 ounces with a standard

deviation of 0.8. Test to see if the mean of the population is at least 12 ounces. Use a .05 level of

significance. 1. The business manager of a local health clinic is interested in estimating the difference between

the fees for extended office visits in their center and the fees of a newly opened group practice.

He gathered the following information regarding the two offices:

Health Clinic Group Practice n1 = 50 visits

= 21 n2 = 45 visits

= 19 S1 = 2.75 S2 = 3.00 x x Test to see if there is a significant difference between the fees charged by the two clinics. Use

a 5% level.

4. A large corporation wants to determine whether or not the ?typing efficiency? course given at

the local college has any influence on the typing speed of their secretaries. A sample of 6

secretaries is selected, and they are sent to take the course. The typing speed of the secretaries in

words per minute ( WPM ) are shown below: Sec?y

1

2

3

4

5

6 WPM Before

65

60

61

63

64

65 WPM After

68

62

66

66

67

67 Use a 5% level and test to see if we can conclude that taking the course will actually increase

the average typing speed of the secretaries.

5. The producer of Viagrow, a plant fertilizer, claims that their bagging equipment is very accurate

and that the standard deviation of all their filled bags is 0.1 ounce or less. A sample of 20 bags

showed a standard deviation of 0.11. Does this sample result confirm the claim of the

manufacturer? Use a 5% level. 6. The salaries of managers at 423 convenience stores is believed to be normally distributed. A

random sample of eighteen managers is chosen. The sample average salary is \$31,520 with a

standard deviation of \$1,560. Find the 95% confidence interval for the average salary of

managers at the 423 convenience stores. 7. Eighteen out of twenty managers at a large discount auto chain have college degrees. Determine

the probability that a random sample of 4 managers contains:

a. Three managers who have college degrees

b. At least three managers who have college degrees

c. No manager has a college degree. 8. A statistics professor wishes to find out the relationship between the classification of a student

and the students? grade in the course. The following is a breakdown of the grades and

classification of students in three sections of the course. (Hint: Transform the raw data below

into marginal and joint probabilities) Grade

A

B

C

D

F First Year

0

0

1

2

0 Sophomore

7

6

7

4

6 Junior

9

8

9

1

2 Senior

10

11

12

4

1 Find:

a. The probability that a randomly selected student makes a D or F in the course.

b. The probability that a randomly selected student is a junior and makes at least a B in the

course.

c. Given that we have randomly selected a senior, what is the probability that they will not

make an A in the course?

9. A local super market has installed a self-service checkout counter. If X is the number of

customers who check out through self-service during a 10 minute period and we assume that the

conditions of the Poisson random variable are satisfied with a mean of 6 customers per 10 minute

period, what is the probability that:

a. Exactly 6 customers will check out during any 10 minute period?

b. No more than 5 customers will check out during any 10 minute period?

c. Exactly 4 customers will check out during any 15 minute period? 10. The following data represent the number of weed-eaters sold per month at the local garden shop

and their prices: (Use the readout below to answer the questions) Price

34

36

32

35

30

38

40 Units sold

3

4

6

5

9

2

1 a. Develop a least squares estimated regression line. Identify the meaning of the slope and

intercept of this estimated line.

b. Could we use this estimate to predict the number of units sold if the price was 25?

c. What hypothesis test is being performed here?

d. What is the meaning of the R2 here? How was this derived? SUMMARY OUTPUT

Regression Statistics

Multiple R

R Square

Standard Error

Observations 0.924982

0.855592

0.826711

1.119949

7 ANOVA

df

Regression

Residual

Total Intercept

Price 1

5

6

Coefficient

s

29.78571

-0.72857 SS

37.15714

6.271429

43.42857

Standard

Error

4.704167

0.13386 MS

37.15714

1.254286 F

29.62415 t Stat

6.331773

-5.44281 P-value

0.001449

0.002842 Significance F

0.002842391

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