Discuss the below:
1. The following data set represents the repair costs (in dollars) for a random sample of 30 dishwashers.
41.82 52.81 57.80 68.16 73.48 78.88 88.13 88.79 90.07 90.35 91.68 91.72 93.01 95.21 95.34 96.50
100.05 101.32 103.59 104.19 105.62 111.32 117.14 118.42
118.77 119.01 120.70 140.52 141.84 147.06
(a) Find the point estimate of the population mean.
(b) Find the maximum error of estimate for a 95% level of confidence.
(c) Construct a 95% confidence interval for the population mean and interpret the results.
2. In a survey of 2000 adults from the U.S. age 65 and over, 1320 received a flu shot.
(a) Find a point estimate for the population proportion p of those receiving flu shots.
(b) Construct a 90% confidence interval for the population proportion.
(c) Find the minimum sample size needed to estimate the population proportion at the 99% confidence level in order to ensure that the estimate is accurate within 4% of the population proportion.
3. Refer to the data set . Assume the population of dishwasher repair costs is normally distributed.
(a) Construct a 95% confidence interval for the population variance.
(b) Construct a 95% confidence interval for the population standard deviation.
4. Interpreting a Decision In Exercises 29-34, consider each claim. If a hypothesis test is performed, how should you interpret a decision that
a) rejects the null hypothesis?
(b) fails to reject the null hypothesis?
5. Gas Mileage
An automotive manufacturer claims the standard deviation for the gas mileage of its models is 3.9 miles per gallon.
6. Writing Hypotheses: Refrigerator Manufacturer A refrigerator manufacturer claims that the mean life of its refrigerators is about 15 years.You are asked to test this claim. How would you write the null hypothesis if
(a) you represent the manufacturer and want to support the claim?
(b) you represent a consumer group and want to reject the claim?
Tea Drinkers A tea drinker's society estimates that the mean consumption of tea by a person in the U.S. is more than 7 gallons per year. In a sample of 100 people, you find that the mean consumption of tea is 7.8 gallons per year with a standard deviation of 2.67 gallons.At can you support the society's claim?
7. Quitting Smoking The number of years it took a random sample of 32 former smokers to quit permanently is listed. At = 0.05, test the claim that the mean time it takes smokers to quit smoking permanently is 15 years.
15.7 13.2 22.6 13.0 10.7 18.1 14.7 7.0 17.3 7.5 21.8
12.3 19.8 13.8 16.0 15.5 13.1 20.7 15.5 9.8 11.9 16.9
7.0 19.3 13.2 14.6 20.9 15.4 13.3 11.6 10.9 21.6
8. Weight Loss A weight loss program claims that program participants have a mean weight loss of at least 10 pounds after one month. You work for a medical association and are asked to test this claim. A random sample of 30 program participants and their weight losses (in pounds) after one month is listed below.At do you have enough evidence to reject the program's claim?
9. Electric Usage You believe the mean annual kilowatt usage of U.S. residential customers is less than 10,000.You do some research and find that a random sample of 30 residential customers has a mean kilowatt usage of 9900 with a standard deviation of 280. You conduct a statistical experiment where and At explain why you cannot reject (Adapted from Edison Electric Institute)
10. Using Different Values of _ and you believe that is not valid.Which of the following allows you to reject ?
(a) Use the same values but increase from 0.01 to 0.02.
(b) Use the same values but increase from 0.01 to 0.03.
(c) Use the same values but increase n from 30 to 50.
(d) Use the same values but increase n from 30 to 100.
Extending the Basics
11. Writing Explain the difference between the classical z-test for and the z-test for m using a P-value.
a
a
H0
H0
H0 .
H0: m Ú 10,000 Ha: m 6 10,000. a = 0.01,
a = 0.03,
a = 0.06,
Hypothesis Testing with One Sample
Weight Loss (in pounds)
after One Month
5 7 7 Key: 5| 7 = 5.7
6 6 7
7 0 1 9
8 2 2 7 9
9 0 3 5 6 8
10 2 5 6 6
11 1 2 5 7 8
12 0 7 8
13 8
14
15 0
12. Microwave Repair Costs A microwave oven repairer says that the mean repair cost for damaged microwave ovens is less than $100.You work for the repairer and want to test this claim.You find that a random sample of five microwave ovens has a mean repair cost of $75 and a standard deviation of $12.50. At ∝ = 0.01 do you have enough evidence to support the repairer's claim?
13. Deciding on a Distribution, decide whether you should use a normal sampling distribution or a t-sampling distribution to perform the hypothesis test. Justify your decision.Then use the distribution to test the claim. Write a short paragraph about the results of the test and what you can conclude about the claim.
14. Gas Mileage A car company says that the mean gas mileage for its luxury sedan is at least 21 miles per gallon (mpg).You believe the claim is incorrect and find that a random sample of 5 cars has a mean gas mileage of 19 mpg and a standard deviation of 4 mpg. Assume the gas mileage of all of the company's luxury sedans is normally distributed. At ∝ = 0.05,test the company's claim.
15. Testing Claims (a) write the claim mathematically and identify H0 and Ha (b) find the critical values and identify the rejection regions, (c) find the standardized test statistic, and (d) decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim
16. Do You Eat Breakfast? A medical researcher estimates that no more than 55% of U.S. adults eat breakfast every day. In a random sample of 250 U.S. adults, 56.4% say that they eat breakfast every day. At ∝ = 0.01is there enough evidence to reject the researcher's claim?
17. Just Say No to GMO An environmentalist claims that more than 50% of British consumers want supermarkets to stop selling genetically modified foods.You want to test this claim.You find that in a random sample of 100 British consumers, 53% say that they want supermarkets to stop selling genetically modified foods. At ∝ = 0.10 can you support the environmentalist's claim?
18. Testing Claims (a) write the claim mathematically and identify and (b) find the critical value(s) and identify the rejection region(s), (c) use the test to find the standardized test statistic, and (d) decide whether to reject or fail to reject the null hypothesis.Then interpret the decision in the context of the original claim. Assume the populations are normally distributed.
19. Life of Appliances A large appliance company estimates that the variance of the life of its appliances is 3.You work for a consumer advocacy group and are asked to test this claim.You find that a random sample of the lives of 27 of the company's appliances has a variance of 2.8. At ∝= 0.05, do you have enough evidence to reject the company's claim?
20. Salaries An employment information service says that the standard deviation of the annual salaries for public relations managers is at least $14,500. The annual salaries for 18 randomly chosen public relations managers are listed. At ∝= 0.10 can you reject the claim?
37,517 50,217 29,177 51,744 69,422 60,770
50,549 50,263 62,939 62,372 65,014 49,164
34,811 55,413 51,310 80,433 34,185 31,805
21. Refer to the data in the following table.The table lists the personal income and outlays (both in trillions of dollars) for Americans for 11 recent years.
Personal Personal
income, x outlays, y
4.5 3.7
4.9 4.0
5.0 4.1
5.3 4.3
5.6 4.6
5.9 4.8
6.2 5.1
6.5 5.4
7.0 5.7
7.4 6.1
7.8 6.5
1. Construct a scatter plot for the data. Do the data appear to have a positive linear correlation, a negative linear correlation, or no linear correlation? Explain.
2. Calculate the correlation coefficient r.What can you conclude?
3. Test the level of significance of the correlation coefficient Use
4. Find the equation of the regression line for the data. Include the regression line in the scatter plot.
5. Use the regression line to predict the personal outlays when the personal income is 5.3 trillion dollars.
6. Find the coefficient of determination and interpret the results.
7. Find the standard error of estimate and interpret the results.
8. Construct a 95% prediction interval for personal outlays when personal income is 6.4 trillion dollars. Interpret the results.
9. The equation used to predict sunflower yield (in pounds) is
y = 1257 - 1.34x1 + 1.41x2
where x1is the number of acres planted (in thousands) and x2 is the number of acres harvested (in thousands). Use the regression equation to predict the values for the given values of the independent variables listed below.Then determine which variable has a greater influence on the value of y
(a) x1 = 2103, x2 = 2037 (b) x1 = 3387, x2 = 3009
(c) x1 = 2185, x2 = 1980 (d) x1 = 3485, x2 = 3404
10. Graphical Analysis use the graph below to answer the question.
1. Use the graph to describe the total variation about a regression line in words and in symbols.
2.Use the graph to describe the unexplained variation about a regression line in words and in symbols.
11. Retail Space and Sales The following table represents the total square footage (in billions) of retailing space at shopping centers and their sales (in billions of U.S. dollars) for 11 years.The equation of the regression line is
Total square footage, x 1.6 2.3 3.0 3.4 3.9 4.6
Sales, y 123.2 211.5 385.5 475.1 641.1 716.9
Total square footage, x 4.7 4.8 4.9 5.0 5.1
Sales, y 768.2 806.6 851.3 893.8 933.9
12. Earnings of Men and Women ? The following table represents median weekly earnings (in U.S. dollars) of full-time male and female workers for five years. The equation of the regression line is
(Source: U.S. Bureau of Labor Statistics)
Median weekly earnings of male workers,x 312 419 485 538 557
Median weekly earnings of female workers,y 201 290 348 406 418
13. Campaign Money ? The money raised and spent (both in millions of U.S. dollars) by all congressional campaigns for eight recent years are shown in the table. The data can be modeled by the regression equation = 1.020x - 25.854. (Source: Federal Election Commission)
Money raised,x 354.7 397.2 472.0 477.6
Money spent,y 342.4 374.1 450.9 459.0
Money raised,x 471.7 659.3 740.5 790.5
Money spent,y 446.3 680.2 725.2 765.3
14. Fund Assets ? The following table represents the total assets (in billions of U.S. dollars) of equity funds and bond and income funds for nine years. The equation of the regression line is = 0.689x + 68.861. (Source: Investment Company Institute)
Equity funds,x 35.9 41.2 77.0 116.9 180.7 Bond and income funds,y 13.1 14 36.6 134.8 273.1
Equity funds,x 249.0 411.6 749.0 1269.0
Bond and income funds,y 304.8 441.4 761.1 798.3
Old Vehicles In, use the information given at the right.
15. Scatter Plot Construct a scatter plot of the data. Show and on the graph.
16. Regression Line Find and graph the regression line.
17. Deviation Calculate the explained deviation, the unexplained deviation, and the total deviation for each data point.
18. Variation Find the (a) explained variation, (b) unexplained variation, and (c) total variation.
19. Coefficient of Determination Find the coefficient of determination. What can you conclude?
20. Error of Estimate Find the standard error of estimate and interpret the results.
21. Prediction Interval Construct a 95% prediction interval for the median age of trucks in use when the median age of cars in use is 7.3.
22. Correlation Coefficient and Slope Recall that the formula for the correlation coefficient r is and the formula for the slope m of a regression line is Given a set of data, why must the slope m of the data's regression line always have the same sign as the data's correlation coefficient r?