A manager wishes to find out whether there is a relationship 2023 Business Finance

2023 1 A manager wishes to find out whether there is a relationship between the number of radio

1. A manager wishes to find out whether there is a relationship between the number of radio ads aired per week and the amount of sales (in thousands of dollars) of a product. The data for the sample are shown below.

a. Draw the scatter plot for the variables.

b. Compute the value of the correlation coefficient.

c. State the hypotheses.

d. Test the significance of the correlation coefficient at .

e. Give a brief explanation of the type of relationship.

2. A store manager wishes to find out whether there is a relationship between the age of her employees and the number of sick days they take each year. The data for the sample are shown below

age x 18 26 39 48 53 58

sick days y 16 12 9 5 6 2

a. Draw the scatter plot for the variables.

b. Compute the value of the correlation coefficient.

c. State the hypotheses.

d. Test the significance of the correlation coefficient at .

e. Give a brief explanation of the type of relationship.

3. Using the number of ads and sales data from question 1:

a. Find the equation of the regression line.

b. Find y when x=7ads

4. Using the age and sick days data from question 2:

a. Find the equation of the regression line.

b. Find y when x = 47 years.

Questions 5 and 6: Do a complete regression analysis by performing the steps below.

Note: No regression should be done when r is not significant.

a. Draw a scatter plot.

b. Compute the correlation coefficient.

c. State the hypotheses.

d. Test the hypotheses at .

e. Determine the regression line equation (if applicable).

f. Plot the regression line on the scatter plot (if applicable).

g. Summarize the results.

5. The data below were obtained for the years 1993 through 1998 and indicate the number of fireworks (in millions) used and the related injuries. Predict the number of injuries (provided there is a significant relationship) if 100 million fireworks are used during a given year

Number of fireworks in use x 67.6 87.1 117 115 118 113

Related injuries y 12.100 12.600 12.500 10.900 7.800 7000

6. A researcher wishes to determine whether a person’s age is related to the number of hours he or she jogs per week. The data for the sample are shown below. Predict the number of hours jogged per week (provided there is a significant relationship) for a 50-year-old person.

Age x 34 22 48 56 62

Hours jogged y 5.5 7 3.5 3 1

7. If r = 0.15, find the coefficients of determination and nondetermination and explain the meaning of each.

8. Using the age and sick days data from question 2, compute the standard error of the estimate.

9. Using the age and sick days data from question 2, find the 98% prediction interval when x = 47 years

10. A random sample of enrollments from public institutions of higher learning (with enrollments under 10,000) is shown below.

West Midwest Northeast south

3737 5585 9264 3903

3706 8205 4673 4539

2457 4170 7320 2649

4309 5440 5401 6414

4103 3355 6050 2935

5048 4412 4087 7147

2463 5115 1579 3354

8739 8669

2431

At , test the claim that the mean enrollments are the same in all parts of the country.

Perform each of the following steps:

a. State the hypotheses and identify the claim.

b. Find the critical value.

c. Compute the test value.

d. Make the decision.

e. Summarize the results.

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