Prob/Stat
AP Statistics Name_________________________________
HW 1 – One Sample Intervals and Tests using the GDC
Directions: Set up the hypothesis. Write the formulas. Use the calculator to find the test statistic and p-val or confidence interval.
1. A recent study claimed that at least 15% of all eighth-grade students are overweight. In a sample of 80 students, 9 were found to be overweight. At ( = 0.10, test the claim.
2. A real estate agent believes that the average closing cost of purchasing a new home is more than $6500 over the purchase price. She selects 40 new home sales at random and finds that the average closing costs are $6600. The standard deviation of the population is $120. Test her belief at ( = 0.05.
3. For a certain age group, a study of 100 people who died showed that 25% had died of cancer. Find the true proportion of individuals who die of cancer in that age group. Use the 98% confidence interval.
4. A bank randomly selected 250 checking-account customers and found that 110 of them also had savings accounts at this same bank. Construct a 95% confidence interval for the true proportion of checking-account customers who also have savings accounts.
5. You wish to conduct a survey in your city to determine the percentage of the drivers who use their seat belts. Find the sample size if you want your estimate to be within 0.02 with 90% confidence.
6. In order to increase customer service, a muffler repair shop claims its mechanics can replace a muffler in less than 12 minutes. A time management specialist selected six repair jobs and found their mean time to be 11.6 minutes with a standard deviation of 2.1 minutes. At ( = 0.02, is there enough evidence to support the shop's claim?
7. A random sample of 12 home prices in a nearby college town found a mean value of $92,460 with a standard deviation of $5200. Find a 95% confidence interval of the mean value of all homes in the college town.
8. In a hospital, a sample of 10 weeks was selected, and the researcher found that an average of 12 babies were born each week. The standard deviation of the sample was 2. Find the 99% confidence interval of the true mean.
9. The National Center for Health Statistics reports that the mean systolic blood pressure for males 35 to 44 years of age is 128 and the standard deviation in this population is 15. The medical director of a large company looks at the medical records of 72 executives in this age group and finds that the mean systolic blood pressure in this sample is 126.07. Is this evidence that the company's executives have a different mean blood pressure from the general public? Test at ( = 0.01.
10. Find the 95% confidence interval for the mean number of ounces of coffee that a machine dispenses in 12ounce cups. Assume the variable is normally distributed. The data is shown below:
12.03 12.10 12.02 11.98 12.00 12.05 11.97
11. A school district in the Midwest believes that they have a group of seventh grade girls who have a greater IQ than average. The average IQ is 100 with a standard deviation of 15. Test at ( = 0.05.
114 100 104 89 102 91 114 114 103 105 108
130 120 132 111 128 118 119 86 72 111 103
12. The manager at Air Express thinks that packages shipped recently weigh less than packages in the past. Records show that in the past packages have had a mean weight of 36.5 lb and a standard deviation of 14.2 lb. A random sample of last month’s shipping records yield the following data. Test at a 1% significance level.
32.1 41.5 16.1 8.9 36.2 12.3 28.4 40.4 45.5 15.2 26.5
13.3 23.5 33.7 18.3 16.3 15.4 39.7 50.3 14.8 44.4 47.7
45.8 52.3 48.4 10.4 59.9 48.1 29.5 22.9 47.9 24.8 20.1
13. In a sample of 60 randomly selected students, only 22 favored the amount budgeted for next year’s intramural and interscholastic sports. Construct the 99% confidence interval for the proportion of all students who support the proposed budget amount.
14. An insurance company states that 90% of its claims are settled within 30 days. A consumer group selected a random sample of 75 of the company’s claims to test this statement. If the consumer group found that 55 of the claims were settled within 30 days, do they have sufficient reason to support their contention that fewer than 90% of the claims are settled within 30 days? Use [pic]
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