Chapter 9 Online Quiz Questions

A noted psychic is tested for ESP. The psychic is presented with 400 cards, all face down, and asked to determine if each card is marked with one of four symbols: a star, a cross, a circle, or a square. The psychic is correct in 120 of the 400 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Suppose we wish to see if there is evidence to suggest that the psychic is doing significantly better than he would be if he were just guessing. To do so, we test H0: p = 0.25 against Ha: p > 0.25. The P-value of the test is

A. 0.0104.

We want to use the t test for a population mean difference μd to test the claim H0: μd = 1. For five paired observations, the differences are 4, -1, 4, 0, and 3. The approximate value of the test statistic in this case is

A. 0.95.

You are thinking of using the t test to test a hypothesis about the mean of a population. A random sample of size n from the population has a slightly skewed distribution with no apparent outliers. For which of the following sample sizes n could you not justify using the t test?

A. 5

On a national compliance test for diabetics, scores have mean μ = 72 and standard deviation σ = 6. A doctor has developed a new program for informing diabetics how to manage the disease and wants to know whether diabetics using this program have a significantly different average score on the test than the national average. For a sample of 60 diabetics who used the program, the sample mean test score was 73.5. A boxplot of the 60 scores reveals considerable skewness. Which of the following statements is true?

A. The P-value of the test is 0.0524.

Suppose we conduct a test of hypotheses and find that the test results are significant at level = 0.025. Which of the following statements then must be true?

A. The results are significant at level = 0.05.

A local teachers' union claims that the average number of school days missed due to illness by the city's school teachers is fewer than 5 per year. A random sample of 28 city school teachers missed an average of 4.5 days last year, with a sample standard deviation of 0.9 days. Assume that "days missed" follow a Normal distribution with mean μ. A test conducted to see whether there is evidence to support the union's claim would have a P-value of

A. between 0.0025 and 0.005.

Which of the following will cause the power of a test to increase?

A. increasing the sample size

Which of the following P-values obtained from a test of hypotheses constitutes the least amount of evidence against the null hypothesis?

B. 0.207

Suppose that we are conducting a test for a population mean μ based on the standard Normal distribution. We originally do a one-sided test but then decide that a two-sided test might be more appropriate (typically, we prefer to use a two-sided test unless there is some reason to believe that an effect in a particular direction exists). How will the results of the test change if we use a two-sided test instead of a one-sided test, assuming that the same data are used?

C. We will require stronger evidence against H0 to reject H0.

We wish to see whether the dial temperature for a certain model of oven is properly calibrated. Four ovens of a certain model are selected at random. The dial on each oven is set to 300°F. After one hour, the actual temperature of each oven is measured. The observed temperatures are 305°, 310°, 300°, and 305°. Assuming that actual temperatures for this model when the dial is set to 300° are Normally distributed with mean μ, we test to see whether the oven is properly calibrated by testing H0: μ = 300 against a two-sided alternative. From the data, the P-value for this test is

C. between 0.05 and 0.10.

A social psychologist reports that "in our sample, ethnocentrism was significantly higher (P < 0.05) among church attendees than among nonattendees." This means that

C. if there were actually no difference in ethnocentrism between church attendees and nonattendees, then the chance that we would have observed a difference at least as extreme as the one we did is less than 5%.

A researcher collects infant mortality data from a random sample of villages in a certain country. It is claimed that the average death rate in this country is the same as that of a neighboring country, which is known to be 17 deaths per 1000 live births. To test this claim using a test of hypotheses, what should the null and alternative hypotheses be?

A. H0: μ = 17, Ha: μ ≠ 17

Does taking garlic tablets twice a day provide significant health benefits? A researcher conducted a study of 50 adult subjects who took garlic tablets twice a day for a period of six months. At the end of the study, 100 variables related to the health of the subjects were measured for each subject, and the means were compared to known means for these variables in the population of all adults. Four of these 100 variables were significantly better (in the sense of statistical significance) at the 5% level for the group taking the garlic tablets compared to the population as a whole. One variable was significantly better at the 1% level for the group taking the garlic tablets compared to the population as a whole. From these results, it would be correct to conclude that

A. there is good statistical evidence that taking garlic tablets twice a day provides some health benefits. B. there is good statistical evidence that taking garlic tablets twice a day provides benefits in the case of the variable that was significant at the 1% level. However, we should be somewhat cautious about making claims for the variables that were significant at the 5% level. C. Neither (A) nor (B) is true C IS THE ANSWER

The distribution of times that a company's technicians take to respond to trouble calls is Normal with mean μ and standard deviation σ = 0.25 hours. The company advertises that its technicians take an average of no more than 2 hours to respond to trouble calls from customers. We wish to conduct a test to assess the amount of evidence against the company's claim. In a random sample of 25 trouble calls, the average amount of time that technicians took to respond was 2.1 hours. From these data, the P-value of the appropriate test is

B. 0.0228.

We wish to test H0: μ = 10 against Ha: μ > 10, where μ is the unknown mean of a Normal population for which the standard deviation σ is also unknown. We draw an SRS of size n = 13 from the population and compute the value of the test statistic, t. From the table of critical values of the t distribution, find the critical value t* that we would compare against the value of t to make a decision about the significance of the test results at significance level = 0.05.

B. 1.782

Suppose that we would like to test H0: μ = 50 against Ha: μ ≠ 50, where μ is the mean of a Normal population, using a test based on the standard Normal distribution. The 95% confidence interval for μ is found to be (51.3, 54.7). Which of the following must then be true?

B. The P-value of the test is at most 0.05.

An advertisement for Chain X, a certain regional supermarket chain, claimed that the chain has had consistently lower prices than its regional competitors. As part of a survey conducted by an independent price-checking company, the average weekly grocery bill (based on the prices of approximately 95 commonly purchased items) was recorded for Chain X and one of its leading competitors during four randomly selected weeks. The bills (rounded to the nearest dollar) were as follows: Week Chainx Competitor 1 255 256 2 241 256 3 232 255 4 234 261 We wish to conduct a test of H0: μd = 0 vs. Ha: μd < 0, where μd = the average difference between the Chain X bill and the competitor's bill during a particular week. (Assume that differences are Normally

B. between 0.025 and 0.05.

The Department of Health plans to test the lead level in a public park. The park will be closed if the lead level exceeds the allowed limit. Otherwise, the park will be kept open. The department conducts the test using soil samples gathered at randomly selected locations. Which of the following decisions would constitute making a Type I error in this situation?

B. closing the park when the average lead level is acceptable

Which of the following would have no effect on the P-value of a z test for a population proportion p?

B. decreasing the significance level of the test,

In a test of hypotheses, the probability that a false null hypothesis should be rejected is also known as the

B. power of the test.

Jamaal, a player on a college basketball team, made only 50% of his free throws last season. During the off-season, he worked on developing a softer shot in the hope of improving his free-throw accuracy. This season, Jamaal made 54 of 95 free throws. Can we conclude that Jamaal's free-throw percentage p this season is significantly different from last year's percentage? The approximate P-value for an appropriate test is

C. 0.1836.

The time that it takes an untrained rat to run a standard maze has a Normal distribution with mean 65 seconds and standard deviation 15 seconds. The researchers want to use a test of hypotheses to determine whether training significantly improves the rats' completion times. An appropriate alternative hypothesis would have the form

C. Ha: μ < 65.

In which of the following situations would it not be appropriate to use the t test for a population mean? (Assume that standard deviations are unknown and Normality conditions are satisfied in all cases; the question relates to whether the procedure itself would be appropriate.)

C. We compare the average blood pressures of independently gathered random samples of men and women.