EBook Problems Hypothesis Proportion

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EBook Problems Set - Testing a Claim about a Proportion

Problem 1

A random sample of 1000 Americans aged 65 and older was collected in 1980 and found that 15% had "hazardous" levels of drinking, which is defined as regularly drinking an amount of alcohol that could cause health problems given the subject's medical conditions. Researchers wanted to know if this proportion has changed since 1980 and so collected a random sample of 1500 Americans aged 65 and older in 2004. They found that 12% drank at hazardous levels. Which of the following is closest to the value of a test statistic that could be used to test the hypothesis that the proportion of hazardous drinkers over the age of 65 has declined since 1980?

  • Choose one answer.
(a) -2.13
(b) 0.014
(c) 0.418
(d) 4.54

Problem 2

Based on past experience, a bank believes that 4% of the people who receive loans will not make payments on time. The bank has recently approved 300 loans. What is the probability that over 6% of these clients will not make timely payments?

  • Choose one answer.
(a) 0.096
(b) 0.038
(c) 0.962
(d) 0.904
(e) 0.017

Problem 3

A marketing director for a radio station collects a random sample of three hundred 18 to 25 year-olds and two hundred and fifty 25 to 40 year-olds. She records the percent of each group that had purchased music online in the last 30 days. She performs a hypothesis test, and the p-value of her test turns out to be 0.15. From this she should conclude:

  • Choose one answer.
(a) there is insufficient evidence to conclude that there is a difference in the proportion of on-line music purchases in the younger and older group.
(b) that about 15% more people purchased on-line music in the younger group than in the older group.
(c) the proportion of on-line music purchasers is the same in the under-25 year-old group as in the older group.
(d) the probability of getting the same results again is .15.

Problem 4

A candidate running for Congress claims that 64% of adults in the U.S. favor a tax cut. Her opponent says this claim is much too high – it is definitely less. To see if this claim has merit, a random sample of 400 adults is asked about it and the percentage favoring a tax cut is obtained. The probability of obtaining the percentage found in the sample or an even lower one turns out to be 0.032, or a 3.2% chance, if one calculates this probability assuming the claim is true. If we test a hypothesis about the candidates’s claim with a 0.05 significance level, based on the outcome of the polling, we should:

  • Choose one answer.
(a) Draw no conclusions and get a bigger sample
(b) Reject the candidate's claim
(c) Conclude that the percentage of adults favoring a tax cut is between 60.8% and 67.2%
(d) Not reject the candidate's claim

Problem 5

Many people sleep in on the weekends to make up for short nights during the work week. The Better Sleep Council reports that 61% of us get more than 7 hours of sleep per night on the weekend. A random sample of 350 adults found that 235 had more than seven hours each night last weekend. At the 0.05 level of significance, does this evidence show that more than 61% of us get seven or more hours off sleep per night on the weekend?

  • Choose one answer.
(a) That cannot be determined without more information
(b) No
(c) Yes

Problem 6

John has just started a tutoring agency. He decides to to take a risk and place a large ad in the Sunday issue of the L.A. Times and hopes that the name recognition is worth the high cost of the ad. He hopes that at least 40% of the neighborhood will recognize the ad. On Monday he contacts 125 randomly selected households who receive the LA Times and he finds that 56 of them had noticed the ad. Would you recommend that John continue to place the ad in the Sunday edition of the L.A. Times?

  • Choose one answer.
(a) Do not put ads in the Sunday Times. Since the p-value of 0.119 is fairly high , we fail to reject the null and there is little evidence that more than 40% of the neighbors recognize the ad.
(b) Do not put ads in the Sunday Times. Since the p-value of 0.238 is large, we fail to reject the null and there is little evidence that more than 40% of the neighbors recognize the ad.
(c) Do not put ads in the Sunday Times. The sample size is not large enough to make such a conclusion; the data are not stable.
(d) Do not place ads in the Sunday Times. In order to spend this kind of money you want to make sure that more than 40% of readers notice the ad.

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