# Computer homework

Management 201 Computer Homework #2

1. Travelocity would like to estimate the current average domestic airfare. The following data shows the airfares for 24 randomly selected tickets for travel within the United States:

$356 $275 $371 $384 $457 $326 $414 $367

$362 $286 $104 $136 $320 $244 $370 $215

$322 $409 $303 $489 $251 $361 $337 $265

a. Construct a 99% confidence interval based on the sample of data

b. What is the margin of error for this sample?

2. According to the Bureau of Labor Statistics, the average hourly wage in the US was $22.57 in May 2010. A random sample of 36 hourly workers was selected during the month. The average wage for this sample was $21.32. Assume the standard deviation of wages for the country is $4.30.

a. Are the results of this sample consistent with the claim made by the Bureau of Labor Statistics using a 95% confidence interval?

b. What is the margin of error for this sample?

3. The Department of Labor would like to estimate the average weekly wages for US adults with a margin of error equal to $20. Determine the sample size needed to construct a confidence interval for this estimate using the following confidence levels. Assume the population standard deviation for the weekly average is $160.

a. 90%

b. 95%

c. 98%

d. Explain why the confidence level effects the sample size needed to obtain a particular margin of error?

4. According to the Mortgage Bankers Association, 10.73% of prime fixed-rate mortgages were in foreclosure or delinquent in the United States during the first quarter of 2010. To validate this claim, a random sample of 700 mortgages was selected, of which 98 were in foreclosure or delinquent

a. Using a 90% confidence interval, does this sample support the findings of the Mortgage Bankers Association?

b. What is the margin of error for this sample?

5. Using a 90% confidence level, The U.S Department of Labor would like to estimate the average weekly hours worked by private employees in the US who are adults. Assume the standard deviation for the number of hours worked is seven hours. Determine the sample sizes needed to construct this confidence interval using the following margins of error

a. Two hours

b. One hour

c. 30 minutes

d. Explain why the margin of error affects the sample size needed to obtain a particular confidence interval.

6. Prior to the release of the iPhone 4 during the summer of 2010, Apple had a 24% share of the smart phone market. Suppose Apple believes that the release of the iPhone 4 will increase the company’s market share. To test this hypothesis, a random sample of 275 smart phone users was selected, 82 of whom owned iPhones. Using alpha=0.05, answer the following questions:

a. State the null and the alternative hypothesis.

b. Based on this sample, what conclusions can be drawn for this test?

c. Determine the p-value for this test and interpret its meaning.

7. Seasons Pizza would like to test the hypothesis that the average delivery time is less than 30 minutes. The following data represents a random sample of delivery times:

23 24 23 36 30 40 34 24 28 29 15 27

Using alpha=0.10 answer the following questions:

a. State the null and alternative hypothesis

b. Does this sample provide enough evidence to support Season’s delivery claim?

c. What assumptions need to be considered for this test?

8. According to a 2010 Business Week Article, the average 401k account balance for individuals nearing retirement was $60,000. To test if this average has changed suppose a random sample of 30 people starting retirement was selected and it was found that the average 401k balance was $67,900. Assume the population standard deviation is $21,000. Using alpha=0.02, answer the following questions:

a. State the null and alternative hypothesis.

b. What conclusions can be made about the current average balance of 401k accounts for people nearing retirement?

c. Determine the p-value for this test and interpret its meaning.

d. If alpha=0.05 had been used rather than alpha=0.02 would the conclusions differ?

9. Average operating time per charge for a 6-volt laptop battery is currently 4-hours. A new claim by SWET technology claims it has developed a new 6-volt battery that has an average charge life that exceeds 4 hours. To test the effectiveness of this new technology, a random sample of 45 batteries was selected and the operating average for these batteries was 5 hours and the sample standard deviation was 2 hours and 30 minutes

a. What is the null and alternative hypothesis

b. What conclusion can be made about the new laptop battery that SWET technology developed using alpha=0.05

c. Determine the p-value for this test.

10. Based on a survey conducted in July 2010, it was found that 32% of the respondents use the same password for all of the social networking websites they log on to. Suppose a follow up survey was conducted in late 2010 to investigate if the proportion has changed. Out of the random sample of 225 internet users, it was found that 86 used the same password for all their social networking websites. Using alpha=0.10 answer the following

a. State the null and alternative hypothesis

b. What conclusions can be made about the proportion of internet users who maintain the same passwords for all social networking sites to which they log on?

11. Before Circuit City declared bankruptcy in 2010, a product manager wanted to investigate the relationship between the price of a new HP Deskjet printer and the demand for it. Every two weeks the price was increased by $5, and demand at a particular store was recorded. Below is the price of and demand data for an HP printer.

**Price Demand**

**$70 18**

**$75 23**

**$80 10**

**$85 16**

**$90 17**

**$95 15**

**$100 5**

a. Construct a scatter plot for this data

b. Calculate the correlation coefficient for this sample

c. Using alpha =0.10, test to determine to determine if the population correlation coefficient is not equal to zero.

12. Answer the following questions using the data from problem 11.

a. Calculate the slope and the y-intercept for the regression equation.

b. Provide an interpretation for the value of the slope.

c. What is the predicted demand for the printer when its price is $87?

13. Answer the following questions using the data from problem 11.

a. Find the sum of squares for the total SST.

b. Calculate the sum of square error SSE

c. Calculate the sum of square of regression SSR

d. Calculate the coefficient of determination

14. Answer the following questions using the data from problem 11.

a. Calculate a 90% confidence interval for the demand of the HP printer when the price is $83.

b. Test whether the regression slope is different from 0 when alpha=0.10

c. Find a 95% confidence interval around the sample slope.

15. Suppose we would like to investigate the relationship between the number of hours students study for a statistical exam and the grades they get for that exam. Below is the sample data from six students who were randomly chosen.

**Hours of study Exam Grade**

**3 86**

**6 95**

**4 92**

**4 83**

**3 78**

**2 79**

a. Calculate the correlation coefficient

b. Calculate the slope and the y-intercept for the regression equation

c. Find the predicted value for exam grade when hours of study=10. What is the problem with this prediction?

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