9-10 Test

. Use Scenario 10-2. When calculating the test statistic, what expression would they use to estimate the standard deviation of the sampling distribution of the difference in proportions, ?

A

Popular wisdom is that eating presweetened cereal tends to increase the number of dental caries (cavities) in children. A sample of children was (with parental consent) entered into a study and followed for several years. Each child was classified as a sweetened-cereal lover or a unsweetened cereal lover. At the end of the study, the amount of tooth damage was measured. Here are the summary data: Cereal preference n Mean Std. Dev. Sweetened 10 6.41 5.0 Unsweetened 15 5.20 15.0 Assuming the necessary conditions for inference are met, which of the following is an approximate 95% confidence interval for the difference in the mean tooth damage? A. B. C. D. E.

A

Phoebe has a theory that older students at her high school are more likely to bring a bag lunch than younger students, because they have grown tired of cafeteria food. She takes a simple random sample of 80 sophomores and finds that 52 of them bring a bag lunch. A simple random sample of 104 seniors reveals that 78 of them bring a bag lunch. Letting p1= proportion of sophomores who bring a bag lunch, and p2= proportion of seniors who bring a bag lunch, Phoebe tests the hypotheses at the α = 0.05 level. ____ 9. Use Scenario 10-4. Phoebe's test statistic is -1.48. Which of the following is closest to the appropriate P-value for the test? A. 0.0808 B. 0.1388 C. 0.9306 D. 0.8612 E. 0.0694

A. 0.0808

1. Use Scenario 10-6. Which of the following is the appropriate test statistic and a possible P-value? A. 1.896, 0.065 B. 1.887, 0.118 C. 1.887, 0.059 D. 1.896, 0.131 E. 1.896, 0.013

A. 1.896, 0.065

7. An appropriate 95% confidence interval for µ has been calculated as ( 0.73, 1.92 ) based on n = 15 observations from a population with a Normal distribution. If we wish to use this confidence interval to test the hypothesis H0: µ = 0 against Ha: µ 0, which of the following is a legitimate conclusion? A. Fail to reject H0 at the = 0.05 level of significance. B. Reject H0 at the = 0.10 level of significance. C. Reject H0 at the = 0.05 level of significance. D. Fail to reject H0 at the = 0.10 level of significance. E. We cannot perform the required test since we do not know the value of the test statistic.

A. Fail to reject H0 at the = 0.05 level of significance.

5. Use Scenario 10-3. Which of the following is the most appropriate conclusion to draw at the α = 0.05 level? A. Fail to reject H0: there is insufficient evidence to conclude that Excellent cures headaches faster than Simple. B. Accept Ha: there is insufficient evidence to conclude that Excellent cures headaches faster than Simple. C. Fail to reject H0: there is sufficient evidence that Excellent cures headaches faster than Simple. D. Reject H0: there is sufficient evidence that Excellent cures headaches faster than Simple. E. Accept Ha: there is sufficient evidence that Excellent cures headaches faster than Simple.

A. Fail to reject H0: there is insufficient evidence to conclude that Excellent cures headaches faster than Simple.

. A significance test was performed to test the null hypothesis H0: µ = 2 versus the alternative Ha: µ 2. A sample of size 28 produced a test statistic is t = 2.051. Assuming all conditions for inference were met, which of the following intervals contains the P-value for this test?

c

A medical researcher is working on a new treatment for a certain type of cancer. After diagnosis, the average survival time on the standard treatment is two years. In an early trial, she tries the new treatment on five subjects and finds that they have an average survival time of four years after diagnosis. Although the survival time has doubled, the results of a t-test for mean survival time are not statistically significant even at the 0.10 significance level. Which of the following is the best course of action for the researcher? A. She should expand her research program to include more subjects—this was a very small sample. B. She should use a z-test instead of a t-test. C. She should increase the significance level of her test so that she rejects the null hypothesis, since the treatment clearly has a positive impact. D. Since the test was not statistically significant, she should abandon study of this treatment and move on to more promising ones. E. She should reexamine her computations—it is likely that she made an error

A. She should expand her research program to include more subjects—this was a very small sample.

Resting pulse rate is an important measure of the fitness of a person's cardiovascular system, with a lower rate indicative of greater fitness. The mean pulse rate for all adult males is approximately 72 beats per minute. A random sample of 25 male students currently enrolled in the Agriculture School at a major university was selected and the mean resting pulse rate was found to be 80 beats per minute with a standard deviation of 20 beats per minute. The experimenter wishes to test if the students are less fit, on average, than the general population. ____ 3. Use Scenario 9-2. The null and alternative hypotheses are ABC OR D

B

All of us nonsmokers can rejoice—the mosaic tobacco virus that affects and injures tobacco plants is spreading! Meanwhile, a tobacco company is investigating if a new treatment is effective in reducing the damage caused by the virus. Eleven plants were randomly chosen. On each plant, one leaf was randomly selected, and one half of the leaf (randomly chosen) was coated with the treatment, while the other half was left untouched (control). After two weeks, the amount of damage to each half of the leaf was assessed. For purposes of comparing the damage, which of the following is the appropriate type of procedure? A. Two-sample t procedures B. Matched pairs t procedures C. Two-sample z procedures D. Two proportion t procedures E. Two-proportion z procedures

B. Matched pairs t procedures

The infamous psychologist, Dr. Visegrips, claims that his secret sleep tapes cause people to become better at basic algebra. "All you have to do," the doctor explains, "is listen to my tapes while you sleep at night, and you'll be better at algebra in two months." A math teacher at a local high school has expressed interest but demands evidence. Five people are randomly selected from students at the school. They take an algebra skills test, listen to Dr. Visegrips' tape for two months while they sleep, and then take a second test. The test scores are as follows: Test scores Person A B C D E Pre-test 68 69 74 71 65 Post-test 70 68 75 72 68 Which of the following conditions must be met in order to use a t-procedure on these paired data? A. Only the distribution of pre-test scores must be approximately Normal. B. Only the distribution of differences (after - before) must be approximately Normal. C. The distribution of pre-test scores and the distribution of differences (after - before) must be approximately Normal. D. The distribution of both pre-test scores and post-test scores must be approximately Normal. E. All three distributions—before, after, and the difference—must be approximately Normal.

B. Only the distribution of differences (after - before) must be approximately Normal.

The water diet requires one to drink two cups of water every half hour from the time one gets up until one goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The weights (in pounds) are Subject A B C D Weight before diet 180 125 240 150 Weight after 6 weeks 170 130 215 152 ____ 13. Use Scenario 9-1. Which of the following conditions must be met in order to use a t-procedure on these paired data? A. The distribution of both pre-diet weights and six-week weights must be approximately Normal. B. Only the distribution of differences (after 6 weeks - before) must be approximately Normal. C. Only the distribution of pre-diet weights must be approximately Normal. D. All three distributions—before diet, after 6 weeks, and the difference—must be approximately Normal. E. The distribution of pre-diet weights and the distribution of differences (after 6 weeks - before) must be approximately Normal.

B. Only the distribution of differences (after 6 weeks - before) must be approximately Normal.

. Use Scenario 10-6. What does power refer to in this situation? A. The ability to not detect an effect of malathion when in fact there is no effect. B. The ability to detect an effect of malathion when in fact there is an effect. C. The ability to not detect an effect of malathion when in fact there is an effect. D. The ability to generalize the results of this controlled experiment to other insect pests besides the cereal leaf beetle. E. The ability to detect an effect of malathion when in fact there is no effect.

B. The ability to detect an effect of malathion when in fact there is an effect.

In a test of H0: µ = 100 against Ha: µ 100, a sample of size 10 produces a sample mean of 103 and a P-value of 0.08. Which of the following is true at the 0.05 level of significance? A. There is sufficient evidence to conclude that µ 100. B. There is insufficient evidence to conclude that µ 100. C. There is sufficient evidence to conclude that µ = 100. D. There is insufficient evidence to conclude that µ = 100. E. There is sufficient evidence to conclude that µ > 103

B. There is insufficient evidence to conclude that µ 100.

A test of produces a sample mean of and a P-value of 0.04. At an α = 0.05 level, which of the following is an appropriate conclusion? A. There is insufficient evidence to conclude that µ = 60. B. There is sufficient evidence to conclude that µ 60. C. There is sufficient evidence to conclude that µ = 60. D. There is sufficient evidence to conclude that µ < 60. E. There is insufficient evidence to conclude that µ 60

B. There is sufficient evidence to conclude that µ 60.

7. Which of the following describes a situation in which it is safe to employ t-procedures A. n1 =35, n2 = 40; both samples are approximately normal, sample 2 has two outliers. B. n1 =6, n2 = 6; both samples are approximately normal. C. n1 =10, n2 = 8; sample 1 is approximately normal, while ample 2 is skewed right. D. n1 =10, n2 = 40; both samples are moderately skewed. E. It is safe to use t-procedures in more than one of the situations above.

B. n1 =6, n2 = 6; both samples are approximately normal.

0. A researcher wishes to determine if people are able to complete a certain pencil and paper maze more quickly while listening to classical music. Suppose previous research has established that the mean time needed for people to complete a certain maze (without music) is 40 seconds. The researcher, therefore, decides to test the hypotheses , where µ = the time in seconds needed to complete the maze while listening to classical music. To do so, the researcher has 10,000 people complete the maze with classical music playing. The mean time for these people is = 39.92 seconds, and the P-value of his significance test is 0.0002. Which statement below best describes the appropriate conclusion to draw from this study? A. The researcher has proved that listening to classical music substantially improves the time it takes to complete the maze. B. The researcher has strong evidence that listening to classical music substantially improves the time it takes to complete the maze. C. Although the researcher has obtained a statistically significant result, it appears to have little practical significance. D. Since the P-value is greater than the reciprocal of the sample size, this is not a significant result. E. The researcher has moderate evidence that listening to classical music substantially improves the time it takes to complete the maze.

C. Although the researcher has obtained a statistically significant result, it appears to have little practical significance.

A medical experiment compared the herb Echinacea with a placebo for preventing colds. The study used 50 different response variables usually associated with colds, such as low-grade fever, congestion, frequency of coughing, etc. The subjects were 40 women between 25 and 40 years of age. ____ 18. Use Scenario 9-3. One response variable was "volume of nasal secretions" (if you have a cold, you blow your nose a lot). Take the average volume of nasal secretions in people without colds to be = 1. An increase to = 3 indicates a cold. Which of the following describes the significance level of a test of versus ? A. The probability that the test fails to reject when = 3 is true. B. The probability that the test fails to reject when = 1 is true. C. The probability that the test rejects when = 1 is true. D. The probability that the test rejects when = 3 is true. E. None of the above

C. The probability that the test rejects when = 1 is true.

You collect test scores on four members of a population which you can safely assume is approximately Normally distributed and test the hypotheses . You obtain a P-value of 0.052. Which of the following statements is true? A. You can accept at the 5% significance level. B. You have failed to obtain any evidence for . C. You can accept at the 10% significance level. D. There is some evidence against , and a study using a larger sample size may be worthwhile. E. At the 5% significance level, you have proved that is true.

D. There is some evidence against , and a study using a larger sample size may be worthwhile.

Different varieties of fruits and vegetables have different amounts of nutrients. These differences are important when these products are used to make baby food. We wish to compare the carbohydrate content of two varieties of peaches. The data were analyzed with MINITAB, and the following output was obtained: N Mean StDev SE Mean Variety 1 5 33.6 3.781 1.691 Variety 2 7 25.0 10.392 3.927 Difference = mu (Variety 1) - mu (Variety 2) Estimate for difference: 8.6 T-Test of difference = 0 (vs not =): T-Value = 2.011 P-Value = 0.0791 DF = 8 ____ 26. Use Scenario 10-1. We wish to test if the two varieties are significantly different in their mean carbohydrate content. Which of the following are the appropriate null and alternative hypotheses for this situation? A. B. C. D. E.

E

A significance test was performed to test the null hypothesis : p = 0.5 versus the alternative Ha: p > 0.5. The test statistic is z = 1.40. Which of the following is closest to the P-value for this test? A. 0.9192 B. 0.1492 C. 0.2984 D. 0.1616 E. 0.0808

E. 0.0808

In a test of H0: p = 0.7 against Ha: p 0.7, a sample of size 80 produces z = 0.8 for the value of the test statistic. Which of the following is closest to the P-value of the test? A. 0.4681 B. 0.2119 C. 0.2090 D. 0.7881 E. 0.4238

E. 0.4238

Janice and her cousin Linda are a little competitive about the relative merits of their home towns. One contest they had was to determine who had more rainy days. They found weather records on the internet and each of them randomly selected 60 days from the past 5 years. Janice found that there had been measurable rainfall on 17 of the 60 days she selected for Asheville, and Linda found that there had been measurable rainfall on 12 of the 60 days she selected for Lincoln. They intend to perform a test of significance on their data, using the hypotheses and the 0.05 significance level. ____ 15. Use Scenario 10-2. Which of the following best describes what it would mean if Janice and Linda's test resulted in a Type I error? A. Choosing the wrong test procedure, such as using a z-test instead of a t-test. B. Concluding that there is no difference in the proportion of rainy days in the two cities when there is a difference. C. Accepting the alternative hypothesis instead of rejecting the null hypothesis. D. Accepting the null hypothesis instead of rejecting the alternative hypothesis. E. Concluding that there is a difference in the proportion of rainy days in the two cities when there is no difference

E. Concluding that there is a difference in the proportion of rainy days in the two cities when there is no difference

Sixty-eight people from a random sample of 128 residents of Uppsala, Sweden, had blue eyes. 45 people from a random sample of 110 people from Preston, England, had blue eyes. Let represent the proportion of people in Uppsala with blue eyes, and let represent the proportion of people in Preston with blue eyes. ____ 1. Use Scenario 10-5. Which of the following conditions are necessary in order to perform the test in Question 1? I. There must be at least 1280 people in Uppsala, Sweden and at least 1100 people in Preston, England. II. np and n(1 - p) must be large enough for Normal calculations to be reasonably accurate. III. Two independent random samples must be taken. A. III only B. I and III are necessary C. I only D. II only E. I, II, and III are all necessary

E. I, II, and III are all necessary

The Excellent Drug Company claims its aspirin tablets will relieve headaches faster than any other aspirin on the market. To determine whether Excellent's claim is valid, 30 volunteers who are suffering from headaches are randomly assigned to two groups. The subjects in one group are given Excellent's aspirin, and the subjects in the other group are given aspirin from the Simple Drug company. The number of minutes required for each subject to recover from the headache is recorded. A 5% significance level test is performed to determine whether Excellent's aspirin cures headaches significantly faster than Simple's aspirin. The data were analyzed with MINITAB, and the following output was obtained: N Mean StDev SE Mean Excellent 15 8.4 4.23 1.092 Simple 15 8.9 4.61 1.190 Difference = mu (Excellent) - mu (Simple) Estimate for difference: -0.5 T-Test of difference = 0 (vs not =): T-Value = -0.380 P-Value = 0.3796 DF = 27.8 ____ 4. Use Scenario 10-3. If the company performing this test committed a Type II error, which of the following describes what happened? A. The company concluded that Excellent aspirin works faster than Simple aspirin when it doesn't. B. The company failed to reject H0 when the P-value was less than α. C. The company rejected H0 when the P-value was greater than α. D. The company concluded that Excellent aspirin works faster than Simple aspirin when it does. E. The company hasn't concluded that Excellent aspirin works faster than Simple aspirin when it does.

E. The company hasn't concluded that Excellent aspirin works faster than Simple aspirin when it does.

The following are percents of fat found in 5 samples of each of two brands of ice cream: A 5.7 4.5 6.2 6.3 7.3 B 6.3 5.7 5.9 6.4 5.1 Which of the following procedures is appropriate to test the hypothesis of equal average fat content in the two types of ice cream? A. Two-proportion z test B. Two-sample t test with 9 df. C. Paired t test with 4 df. D. Paired t test with 5 df. E. Two-sample t test with 4 df

E. Two-sample t test with 4 df

We want to test H0: µ = 1.5 vs. Ha : µ 1.5 at = 0.05 . A 95% confidence interval for µ calculated from a given random sample is (1.4, 3.6). Based on this finding we A. cannot make any decision at all because the value of the test statistic is not available. B. cannot make any decision at all because (1.4, 3.6) is only a 95% confidence interval for µ. C. cannot make any decision at all because the distribution of the population is unknown. D. reject H0 . E. fail to reject H0 .

E. fail to reject H0 .