Testing the 123-Gallon Daily Water Claim: Fact or Fiction?

In what ways is the t distribution similar to the standard normal distribution? In what ways is the t distribution different from the standard normal distribution?

What are the degrees of freedom for the t test?

Find the critical value (or values) for the t test for each. a. n _ 10, a _ 0.05, right-tailed _1.833 b. n _ 18, a _ 0.10, two-tailed 1.740 c. n _ 6, a _ 0.01, left-tailed _3.365 d. n _ 9, a _ 0.025, right-tailed _2.306 e. n _ 15, a _ 0.05, two-tailed 2.145 f. n _ 23, a _ 0.005, left-tailed _2.819 g. n _ 28, a _ 0.01, two-tailed 2.771 h. n _ 17, a _ 0.02, two-tailed 2.583

(ans) Using Table F, find the P-value interval for each test value. a. t _ 2.321, n _ 15, right-tailed b. t _ 1.945, n _ 28, two-tailed c. t__1.267, n _ 8, left-tailed d. t _ 1.562, n _ 17, two-tailed e. t _ 3.025, n _ 24, right-tailed f. t__1.145, n _ 5, left-tailed g. t _ 2.179, n _ 13, two-tailed h. t _ 0.665, n _ 10, right-tailed

Veterinary Expenses of Cat Owners According to the American Pet Products Manufacturers Association, cat owners spend an average of $179 annually in routine veterinary visits. A random sample of local cat owners revealed that 10 randomly selected owners spent an average of $205 with s _ $26. Is there a significant statistical difference at a _ 0.01? Source: www.hsus.org/pets

Park Acreage A state executive claims that the average number of acres in western Pennsylvania state parks is less than 2000 acres. A random sample of five parks is selected, and the number of acres is shown. At a _ 0.01, is there enough evidence to support the claim? 959 1187 493 6249 541 Source: Pittsburgh Tribune-Review.

Cell Phone Call Lengths The average local cell phone call length was reported to be 2.27 minutes. A random sample of 20 phone calls showed an average of 2.98 minutes in length with a standard deviation of 0.98 minute. At a _ 0.05 can it be concluded that the average differs from the population average? Source: World Almanac.

Commute Time to Work A survey of 15 large U.S. cities finds that the average commute time one way is 25.4 minutes. A chamber of commerce executive feels that the commute in his city is less and wants to publicize this. He randomly selects 25 commuters and finds the average is 22.1 minutes with a standard deviation of 5.3 minutes. At \(\alpha=0.10\), is he correct?

Heights of Tall Buildings A researcher estimates that the average height of the buildings of 30 or more stories in a large city is at least 700 feet. A random sample of 10 buildings is selected, and the heights in feet are shown. At a _ 0.025, is there enough evidence to reject the claim? 485 511 841 725 615 520 535 635 616 582 Source: Pittsburgh Tribune-Review.

Exercise and Reading Time Spent by Men Men spend an average of 29 minutes per day on weekends and holidays exercising and playing sports. They spend an average of 23 minutes per day reading. A random sample of 25 men resulted in a mean of 35 minutes exercising with a standard deviation of 6.9 minutes and an average of 20.5 minutes reading with s _ 7.2 minutes. At a _ 0.05 for both, is there sufficient evidence that these two results differ from the national means? Source: Time magazine.

Television Viewing by Teens Teens are reported to watch the fewest total hours of television per week of all the demographic groups. The average television viewing for teens on Sunday from 1:00 to 7:00 P.M. is 1 hour 13 minutes. Arandom sample of local teens disclosed the following times for Sunday afternoon television viewing. At a _ 0.01 can it be concluded that the average is greater than the national viewing time? (Note: Change all times to minutes.) 2:30 2:00 1:30 3:20 1:00 2:15 1:50 2:10 1:30 2:30 Source: World Almanac.

Internet Visits A U.S. Web Usage Snapshot indicated a monthly average of 36 Internet visits per user from home. A random sample of 24 Internet users yielded a sample mean of 42.1 visits with a standard deviation of 5.3. At the 0.01 level of significance can it be concluded that this differs from the national average? Source: New York Times Almanac.

Cost of Making a Movie During a recent year the average cost of making a movie was $54.8 million. This year, a random sample of 15 recent action movies had an average production cost of $62.3 million with a variance of $90.25 million. At the 0.05 level of significance, can it be concluded that it costs more than average to produce an action movie? Source: New York Times Almanac.

Chocolate Chip Cookie Calories The average 1-ounce chocolate chip cookie contains 110 calories. A random sample of 15 different brands of 1-ounce chocolate chip cookies resulted in the following calorie amounts. At the \(\alpha= 0.01\) level, is there sufficient evidence that the average calorie content is greater than 110 calories? 100 125 150 160 185 125 155 145 160 100 150 140 135 120 110 Source: The Doctor’s Pocket Calorie, Fat, and Carbohydrate Counter.

Cell Phone Bills The average monthly cell phone bill was reported to be $50.07 by the U.S. Wireless Industry. Random sampling of a large cell phone company found the following monthly cell phone charges: 55.83 49.88 62.98 70.42 60.47 52.45 49.20 50.02 58.60 51.29 At the 0.05 level of significance can it be concluded that the average phone bill has increased? Source: World Almanac.

Water Consumption The Old Farmers Almanac stated that the average consumption of water per person per day was 123 gallons. To test the hypothesis that this figure may no longer be true, a researcher randomly selected 16 people and found that they used on average 119 gallons per day and s _ 5.3. At a _ 0.05, is there enough evidence to say that the Old Farmers Almanac figure might no longer be correct? Use the P-value method.

Doctor Visits A report by the Gallup Poll stated that on average a woman visits her physician 5.8 times a year. A researcher randomly selects 20 women and obtained these data. 3 2 1 3 7 2 9 4 6 6 8 0 5 6 4 2 1 3 4 1 At \(\alpha = 0.05\) can it be concluded that the average is still 5.8 visits per year? Use the P-value method.

Number of Jobs The U.S. Bureau of Labor and Statistics reported that a person between the ages of 18 and 34 has had an average of 9.2 jobs. To see if this average is correct, a researcher selected a sample of 8 workers between the ages of 18 and 34 and asked how many different places they had worked. The results were as follows: 8 12 15 6 1 9 13 2 At a _ 0.05 can it be concluded that the mean is 9.2? Use the P-value method. Give one reason why the respondents might not have given the exact number of jobs that they have worked.

Teaching Assistants Stipends A random sample of stipends of teaching assistants in economics is listed. Is there sufficient evidence at the a _ 0.05 level to conclude that the average stipend differs from $15,000? The stipends listed (in dollars) are for the academic year. 14,000 18,000 12,000 14,356 13,185 13,419 14,000 11,981 17,604 12,283 16,338 15,000 Source: Chronicle of Higher Education.

Average Family Size The average family size was reported as 3.18. A random sample of families in a particular school district resulted in the following family sizes: 5 4 5 4 4 3 6 4 3 3 5 6 3 3 2 7 4 5 2 2 2 3 5 2 At a _ 0.05, does the average family size differ from the national average? Source: New York Times Almanac.