ST 511 Cumulative Exam - Lecture 6

c and d

A large midwestern state administers a statewide mathematics exam that has an average of 500. A researcher is designing a study to test the idea that students from charter schools score higher than average on the test. The researcher plans to take a random sample of 100 students from charter schools. He will then carry out a test of hypothesis using a significance level of 0.01. Which of the following will increase the power of this test? (Pick all that apply, even if they are not the recommended way to increase power.) Select one or more: a) If the researcher talks with 50 students. b) If the researcher uses a significance level of 0.001. c) If the researcher talks with 500 students. d) If the researcher uses a significance level of 0.05.

c and d

A pharmaceutical company has developed a new drug to help people fall asleep faster. A competing drug claims that it helps people fall asleep 30 minutes faster, on average. This company wishes to test the hypothesis that their drug helps people fall asleep even faster than that: Ho: μ = 30 vs. Ha: μ > 30. Define a Type I and a Type II Error in this context. Select one or more: a) A Type II Error would be the company deciding their drug does help people fall asleep faster (than the competitor) when in fact it does not. b) A Type I Error would be the company deciding their drug does not help people fall asleep faster (than the competitor) when in fact it does. c) A Type I Error would be the company deciding their drug does help people fall asleep faster (than the competitor) when in fact it does not. d) A Type II Error would be the company deciding their drug does not help people fall asleep faster (than the competitor) when in fact it does.

b

A student group claims that first-year students at a university should study 2.5 hours (150 minutes) per night during the school week. A skeptic suspects that they study less than that on the average. A survey of 51 randomly selected students finds that on average students study 140 minutes per night with a standard deviation of 30 minutes. What conclusion can be made from this data? Select one: a. We do not have enough information to make a conclusion about this study. b. The p-value is less than .05, therefore we conclude that students study less than 150 minutes per night. c. The p-value is greater than .05, therefore we do not have enough evidence to conclude that students study less than 150 minutes per night. d. The p-value is less than .05, therefore we do not have enough evidence to conclude that students study less than 150 minutes per night. e. The p-value is less than .05, therefore we conclude that students study greater than 150 minutes per night.

c and d

An allergist wishes to test the hypothesis that at least 30% of the public is allergic to some cheese products. Define Type I and Type II Errors in this context. Select one or more: a) A Type II Error would be made if the allergist concludes that at least 30% of the public are allergic to these cheese products when, in fact, fewer than 30% are allergic. b) A Type I Error would be made if the allergist concludes that fewer than 30% of the public are allergic to these cheese products when, in fact, 30% or more are allergic. c) A Type II Error would be made if the allergist concludes that fewer than 30% of the public are allergic to these cheese products when, in fact, 30% or more are allergic. d) A Type I Error would be made if the allergist concludes that at least 30% of the public are allergic to these cheese products when, in fact, fewer than 30% are allergic.

a and b

Consider the drug testing hypotheses from the previous question. Define statistical power in the context of this problem. Select one or more: a) Power would be the probability the company decides their drug does help people fall asleep faster (than the competitor) when in fact it does. b) Power would be the probability of not making a Type II Error. c) Power would be the probability of not making a Type I Error. d) Power would be the probability the company decides their drug does not help people fall asleep faster (than the competitor) when in fact it does not.

d

Suppose a hypothesis test for a population mean is correctly conducted and the decision is made to not reject the null hypothesis. What type of error could have been made? Select one: a. Neither type of error could have been made if the test was conducted correctly. b. Either type of error could have been made. c. A Type I Error d. A Type II Error

b

The p-value is the probability that the null hypothesis is true. Select one: a. True b. False

c

psychology student conducted a research study in which the research question is whether financial incentives can improve performance on video games.The student prepares an experiment in which 40 subjects are randomly assigned to one of two groups.The first group was offered $5 for a score above 100 and the other group was simply told to "do your best." She collects data and conducts the appropriate hypothesis test. Which of the following would be the best interpretation of the p-value from her test? Select one: a. The p-value is the probability that the $5 incentive is really helpful. b. The p-value is the probability that the $5 incentive is not really helpful. c. The p-value is the probability that she would get a test statistic as extreme as the one she actually found, if the $5 incentive is really not helpful. d. The p-value is the probability that a student wins on the video game.

b

researcher wanted to know if there was a difference in the number of microscopic particles in bottled water versus filtered tap water. A typical glass of water has hundreds of millions of microscopic particles in it. Her study found a mean difference of 12 microscopic particles between bottled and filtered tap water which had a p-value of .55. What should we conclude about the results of this study? Select one: a. The results were statistically significant but not practically significant. b. The results were neither statistically significant nor practically significant. c. The results were both statistically significant and practically significant. d. The results were practically significant but not statistically significant.