6/19/13 Practice problems on ch 8 and ch 11

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1 6/19/13 Practice problems on ch 8 and ch 11 For all hypotheses test you must do the following: z/t test a. State the hypotheses and identify the claim. b. Find the critical values. c. Compute the test statistic. d. Make a decision. e. Summarize the results. P-value a. State the hypotheses and identify the claim. b. Compute the test statistic. c. Find P-value d. Make a decision. e. Summarize the results. 1. Nationwide, the average waiting time until a electric utility customer service representative answers a call is 260 seconds. The Gigantic Kilowatt Energy Company randomly sampled 50 calls and found that, on average, they were answered in 225 seconds with a population standard deviation of 25 seconds. Can the company claim that they are faster than the average utility at α = 0.05? 2. Dr. Christina Cuttleman, a nutritionist, claims that the average number of calories in a serving of popcorn is 75 with a standard deviation of 7. A sample of 50 servings of popcorn was found to have an average of 78 calories. Check Dr. Cuttleman's claim at α = The average magnesium concentration in ground water around Metro City is µ = 59.6 parts per million (ppm) with a standard deviation of σ = 12. The table below shows the ground-water magnesium concentrations (ppm) from random sites in a suburb located 15 miles away. At α = 0.10, can it be concluded that the average magnesium concentration in the suburb differs from 59.6 ppm? A manufacturer claims that its televisions have an average lifetime of at least five years (60 months) with a population standard deviation of seven months. Eighty-one televisions were selected at random, and the average lifetime was found to be 59 months. With α = 0.025, is the manufacturer's claim supported? Page 1

2 5. Reginald Brown, an inspector from the Department of Weights and Measures, weighed 15 eighteen-ounce cereal boxes of corn flakes. He found their mean weight to be 17.8 ounces with a standard deviation of 0.4 ounces. At α = 0.01, are the cereal boxes lighter than they should be? 6. The national average of times a person checks their is 46.4 times per month. A random sample of 20 people yielded a mean of checks per month with a standard deviation of 5.3. At the 0.05 level of significance can it be concluded that this differs from the national average? 7. Science fiction novels average 270 pages in length. The average length of 10 randomly chosen novels written by I. M. Wordy was 285 pages in length with a standard deviation of 30. At α =.05, are Wordy's novels significantly longer than the average science fiction novel? 8. A random group of seniors was selected from a university and asked about their plans for the following year. The school advising office claims that 50% of the students plan to work, 25% of the students plan to continue in school, and 25% of the students plan to take some time off. Is there evidence to reject this hypothesis at α = 0.05? Plans Work School Time off Number of students A random group of customers at a fast food chain were asked whether they preferred hamburgers, chicken sandwiches, or fish sandwiches. The restaurant's marketing department claims that 40% of customers prefer hamburgers, 42% of the customers prefer chicken sandwiches, and 18% of the customers prefer fish sandwiches. Is there evidence to reject this hypothesis at α = 0.05? Plans Hamburgers Chicken Fish Number of students A random group of apartments was selected from a city to analyze the number of bedrooms they have. Is there evidence to reject the hypothesis that the apartments are equally distributed between 1-bedroom, 2-bedroom, and 3-bedroom apartments, at α = 0.05? Year in school 1 bedroom 2 bedrooms 3 bedrooms Number of students A random group of students was selected from a large student conference to analyze their class in school. Is there evidence to reject the hypothesis that the number of students is equally distributed between the four classes, at α = 0.05? Year in school Freshman Sophomore Junior Senior Number of students Page 2

3 12. A random group of oranges were selected from an orchard to analyze their ripeness. Based on the time of year, the orchard owner believes that 25% of the oranges are ready for picking now, 30% will be ready in three days, 25% will be ready in one week, and 20% will be ready in two weeks. Is there evidence to reject this hypothesis at α = 0.05? Ready to pick Ripe Ready in three days Ready in one week Ready in two weeks Number of oranges A random group of used books was selected from book warehouse to analyze their condition. The book store believes that 24% of the books are in excellent condition, 34% are in very good condition, 19% are in fair condition, and 23% are in poor condition. Is there evidence to reject this hypothesis at α = 0.05? Book condition Excellent Very good Fair Poor Number of books Two computer stores recorded the number of computers sold in a week along with the sizes of their hard drives. At α = 0.05, test the claim that the distribution of hard drives and the store where the computers were bought are not related. Number of computers 20 GB drive 40 GB drive 80 GB drive 160 GB drive Store Store The table lists the number of students from three different high schools participating in the mathematics and physics sections of a science fair. At α = 0.05, test the claim that the section of participation and the high school where the students were from are independent. Number of Students High School 1 High School 2 High School 3 Mathematics Physics Page 3

4 Answer Key 1. Yes, because the test value 9.90 falls in the critical region. 2. H : µ = 75 0 (the claim) and H : µ 75 1 Critical values: ±1.96 Test value: 3.03 Reject the null hypothesis. There is not enough evidence to support the claim that the average number of calories in a serving of popcorn is a. Ho : µ = 59.6 ppm and H : µ 59.6 ppm (claim) 1 b. C.V. = ± 1.96 c. z = 5.5 ( x = roundpv(xbar,?3) ppm ) d. Reject the null hypothesis. e. There is evidence to support the claim that the suburb's average magnesium concentration differs from Metro City's. 4. H0 : µ = 60 (claim) and H1: µ < 60 Critical value = 1.96 Test value = 1.29 Do not reject the claim since the test value falls in the noncritical region. There is not enough evidence to reject the manufacturer's claim that his televisions have an average lifetime of at least five years. 5. H0 : µ = 18.0 (claim) and H1: µ < 18.0 Critical value: Test value: 1.94 Do not reject the claim since 1.94 does not fall within the critical region. There is not enough evidence to reject the claim that the cereal boxes weigh 18 ounces. 6. For a test value of 2.36, look at the table: we see 0.02 < P-value < 0.05, the P-value is < Reject the null hypothesis. 7. H0 : µ = 270 and H1: µ > 270 (claim) Critical value: Test value: The conclusion is to not reject the null hypothesis. There is not enough evidence to support the claim that Wordy's novels are longer than the average science fiction novel. 8. There is not evidence to reject the claim that the students' plans are distributed as claimed because the test value < There is not evidence to reject the claim that the customers' preferences are distributed as claimed because the test value < There is not evidence to reject the claim that the apartments are equally distributed between the three sizes because the test value < There is not evidence to reject the claim that students are equally distributed between the four classes because the test value < There is not evidence to reject the claim that the oranges are distributed as claimed because the test value < There is not evidence to reject the claim that the books are distributed as claimed because the test value < There is evidence to reject the claim that the size of hard drive sold and the store number are not related because the test value > There is evidence to reject the claim that the high school and the section of participation are independent because the test value > Page 4

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