Warming and Ice Melt The average depth of the Hudson Bay

Warming and Ice Melt The average depth of the Hudson Bay is 305 feet. Climatologists were interested in seeing if the effects of warming and ice melt were affecting the water level. Fifty-five measurements over a period of weeks yielded a sample mean of 306.2 feet. The population variance is known to be 3.57. Can it be concluded at the 0.05 level of significance that the average depth has increased? Is there evidence of what caused this to happen? Source: World Almanac and Book of Facts 2010.

Credit Card Debt It has been reported that the average credit card debt for college seniors at the college book store for a specific college is $3262. The student senate at a large university feels that their seniors have a debt much less than this, so it conducts a study of 50 randomly selected seniors and finds that the average debt is $2995, and the population standard deviation is $1100. With \(\alpha= 0.05\), is the student senate correct?

Revenue of Large Businesses Aresearcher estimates that the average revenue of the largest businesses in the United States is greater than $24 billion.Asample of 50 companies is selected, and the revenues (in billions of dollars) are shown. At a _ 0.05, is there enough evidence to support the researchers claim? Assume s _ 28.7. 178 122 91 44 35 61 56 46 20 32 30 28 28 20 27 29 16 16 19 15 41 38 36 15 25 31 30 19 19 19 24 16 15 15 19 25 25 18 14 15 24 23 17 17 22 22 21 20 17 20 Source: New York Times Almanac.

Moviegoers The average moviegoer sees 8.5 movies a year. A moviegoer is defined as a person who sees at least one movie in a theater in a 12-month period. A random sample of 40 moviegoers from a large university revealed that the average number of movies seen per person was 9.6. The population standard deviation is 3.2 movies. At the 0.05 level of significance, can it be concluded that this represents a difference from the national average? Source: MPAA Study.

Nonparental Care According to the Digest of Educational Statistics, a certain group of preschool children under the age of one year each spends an average of 30.9 hours per week in nonparental care. A study of state university center-based programs indicated that a random sample of 32 infants spent an average of 32.1 hours per week in their care. The standard deviation of the population is 3.6 hours. At a_0.01 is there sufficient evidence to conclude that the sample mean differs from the national mean?

Peanut Production inVirginia The average production of peanuts inVirginia is 3000 pounds per acre.Anew plant food has been developed and is tested on 60 individual plots of land. The mean yield with the new plant food is 3120 pounds of peanuts per acre, and the population standard deviation is 578 pounds. At a_0.05, can you conclude that the average production has increased? Source: The Old Farmers Almanac.

Heights of 1-Year-Olds The average 1-year-old (both genders) is 29 inches tall. A random sample of 30 1-year-olds in a large day care franchise resulted in the following heights. At \(\alpha= 0.05\), can it be concluded that the average height differs from 29 inches? Assume \(\sigma= 2.61\). 25 32 35 25 30 26.5 26 25.5 29.5 32 30 28.5 30 32 28 31.5 29 29.5 30 34 29 32 27 28 33 28 27 32 29 29.5 Source: www.healthepic.com

Salaries of Government Employees The mean salary of federal government employees on the General Schedule is $59,593. The average salary of 30 state employees who do similar work is $58,800 with s _ $1500. At the 0.01 level of significance, can it be concluded that state employees earn on average less than federal employees? Source: New York Times Almanac.

Operating Costs of an Automobile The average cost of owning and operating an automobile is $8121 per 15,000 miles including fixed and variable costs. Arandom survey of 40 automobile owners revealed an average cost of $8350 with a population standard deviation of $750. Is there sufficient evidence to conclude that the average is greater than $8121? Use a _ 0.01. Source: New York Times Almanac 2010.

For Exercises 1 through 13, perform each of the following steps. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Home Prices in Pennsylvania A real estate agent claims that the average price of a home sold in Beaver County, Pennsylvania, is $60,000. A random sample of 36 homes sold in the county is selected, and the prices in dollars are shown. Is there enough evidence to reject the agent’s claim at \(\alpha = 0.05\)? Assume \(\sigma = $76,025\).

Use of Disposable Cups The average college student goes through 500 disposable cups in a year. To raise environmental awareness, a student group at a large university volunteered to help count how many cups were used by students on their campus.Arandom sample of 50 students results found that they used a mean of 476 cups with s_42 cups. At a_0.01, is there sufficient evidence to conclude that the mean differs from 500? Source: www.esc.mtu.edu/SFES.php

Student Expenditures The average expenditure per student (based on average daily attendance) for a certain school year was $10,337 with a population standard deviation of $1560. A survey for the next school year of 150 randomly selected students resulted in a sample mean of $10,798. Do these results indicate that the average expenditure has changed? Choose your own level of significance. Source: World Almanac.

Ages of U.S. Senators The mean age of Senators in the 109th Congress was 60.35 years. A random sample of 40 senators from various state senates had an average age of 55.4 years, and the population standard deviation is 6.5 years. At a _ 0.05, is there sufficient evidence that state senators are on average younger than the Senators in Washington? Source: CG Today.

What is meant by a P-value? The P-value is the actual probability of getting the sample mean if the null hypothesis is true.

State whether the null hypothesis should be rejected on the basis of the given P-value. a. P-value _ 0.258, a _ 0.05, one-tailed test b. P-value _ 0.0684, a _ 0.10, two-tailed test c. P-value _ 0.0153, a _ 0.01, one-tailed test d. P-value _ 0.0232, a _ 0.05, two-tailed test Reject. e. P-value _ 0.002, a _ 0.01, one-tailed test Reject.

Soft Drink Consumption A researcher claims that the yearly consumption of soft drinks per person is 52 gallons. In a sample of 50 randomly selected people, the mean of the yearly consumption was 56.3 gallons. The standard deviation of the population is 3.5 gallons. Find the P-value for the test. On the basis of the P-value, is the researchers claim valid? Source: U.S. Department of Agriculture.

Stopping Distances A study found that the average stopping distance of a school bus traveling 50 miles per hour was 264 feet. A group of automotive engineers decided to conduct a study of its school buses and found that for 20 buses, the average stopping distance of buses traveling 50 miles per hour was 262.3 feet. The standard deviation of the population was 3 feet. Test the claim that the average stopping distance of the companys buses is actually less than 264 feet. Find the P-value. On the basis of the P-value, should the null hypothesis be rejected at a _ 0.01? Assume that the variable is normally distributed. Source: Snapshot, USA TODAY.

Copy Machine Use A store manager hypothesizes that the average number of pages a person copies on the stores copy machine is less than 40. A sample of 50 customers orders is selected. At a _ 0.01, is there enough evidence to support the claim? Use the P-value hypothesis-testing method. Assume s _ 30.9. 2 2 2 5 32 5 29 8 2 49 21 1 24 72 70 21 85 61 8 42 3 15 27 113 36 37 5 3 58 82 9 2 1 6 9 80 9 51 2 122 21 49 36 43 61 3 17 17 4 1

Burning Calories by Playing Tennis Ahealth researcher read that a 200-pound male can burn an average of 546 calories per hour playing tennis. Thirtysix males were randomly selected and tested. The mean of the number of calories burned per hour was 544.8. Test the claim that the average number of calories burned is actually less than 546, and find the P-value. On the basis of the P-value, should the null hypothesis be rejected at a _ 0.01? The standard deviation of the population is 3. Can it be concluded that the average number of calories burned is less than originally thought?

Breaking Strength of Cable A special cable has a breaking strength of 800 pounds. The standard deviation of the population is 12 pounds. A researcher selects a sample of 20 cables and finds that the average breaking strength is 793 pounds. Can he reject the claim that the breaking strength is 800 pounds? Find the P-value. Should the null hypothesis be rejected at a _ 0.01? Assume that the variable is normally distributed.

Farm Sizes The average farm size in the United States is 444 acres. A random sample of 40 farms in Oregon indicated a mean size of 430 acres, and the population standard deviation is 52 acres. At a _ 0.05, can it be concluded that the average farm in Oregon differs from the national mean? Use the P-value method. Source: New York Times Almanac.

Farm Sizes Ten years ago, the average acreage of farms in a certain geographic region was 65 acres. The standard deviation of the population was 7 acres.Arecent study consisting of 22 farms showed that the average was 63.2 acres per farm. Test the claim, at a_0.10, that the average has not changed by finding the P-value for the test. Assume that s has not changed and the variable is normally distributed.

Transmission Service A car dealer recommends that transmissions be serviced at 30,000 miles. To see whether her customers are adhering to this recommendation, the dealer selects a sample of 40 customers and finds that the average mileage of the automobiles serviced is 30,456. The standard deviation of the population is 1684 miles. By finding the P-value, determine whether the owners are having their transmissions serviced at 30,000 miles. Use a _ 0.10. Do you think the a value of 0.10 is an appropriate significance level?

Speeding Tickets A motorist claims that the South Boro Police issue an average of 60 speeding tickets per day. These data show the number of speeding tickets issued each day for a period of one month. Assume s is 13.42. Is there enough evidence to reject the motorists claim at a _ 0.05? Use the P-value method. 72 45 36 68 69 71 57 60 83 26 60 72 58 87 48 59 60 56 64 68 42 57 57 58 63 49 73 75 42 63

Sick Days Amanager states that in his factory, the average number of days per year missed by the employees due to illness is less than the national average of 10. The following data show the number of days missed by 40 employees last year. Is there sufficient evidence to believe the managers statement at a_0.05? s _ 3.63. Use the P-value method. 0 6 12 3 3 5 4 1 3 9 6 0 7 6 3 4 7 4 7 1 0 8 12 3 2 5 10 5 15 3 2 5 3 11 8 2 2 4 1 9

Suppose a statistician chose to test a hypothesis at a _ 0.01. The critical value for a right-tailed test is _2.33. If the test value were 1.97, what would the decision be? What would happen if, after seeing the test value, she decided to choose a _ 0.05? What would the decision be? Explain the contradiction, if there is one.

Hourly Wage The president of a company states that the average hourly wage of her employees is $8.65. A sample of 50 employees has the distribution shown. At a _ 0.05, is the presidents statement believable? Assume s _ 0.105. Class Frequency 8.358.43 2 8.448.52 6 8.538.61 12 8.628.70 18 8.718.79 10 8.808.88 2