Statistics Final

At one standardized test site, students taking the test for a second time volunteered to inhale supplemental oxygen for 10 minutes before the test. In fact, some received oxygen, but others (randomly assigned) were given just normal air. Test results showed that 42 of 66 students who breathed oxygen improved their test scores, compared to only 35 of 63 students who did not get the oxygen. Which procedure should researchers use to see if there is evidence that breathing extra oxygen can help test-takers think more clearly? a) Matched pairs t-test b) 2-sample t-test c) 1-proportion z-test d) 2-proportion z-test

d) 2-propotion z-test

A survey question asked students "How many hours of TV do you watch per week?" Using their responses, a researcher wants to estimate the difference in mean hours between high school and middle school students. What should the researcher use? a) Matched pairs t-interval b) 2-proportion z-interval c) 1-sample t-interval d) 2-sample t-interval

d) 2-sample t-interval

A truck company wants an on-time delivery for 98% of the parts they order from a metal manufacturing plant. They have been ordering from a particular steel company but will switch to a new, cheaper manufacturer unless there is evidence that this new manufacturer cannot meet 98% on-time goal. As a test the truck company purchases a random sample of metal parts from the cheaper manufacturer, and then determines if these parts were delivered on-time. Which hypothesis should they test? a) H0: p> 0.98 HA: p= 0.98 b) H0: p=0.98 HA: p≠ 0.98 c) H0: p= 0.98 HA: p< 0.98 d) H0: p=0.98 HA: p> 0.98

c) H0: p = 0.98 HA: p < 0.98

Which of the following is true about student's t-models? I. They are unimodal, symmetric, and bell shaped. II. They have fatter tails than the normal model. III. As the degrees of freedom increase, the t-models look more and more like the normal. a) II and III b) I and II c) I, II, and III d) I and III

c) I, II, and III

A philosophy professor wants to find out whether the mean age of the men in his large lecture class is equal to the mean age of women in his class. After collecting data from a random sample of his students, the professor tested the hypothesis H0: μ M - μ W = 0 against the alternative μ M - μ W ≠ 0. The p-value for the test was 0.003. Which is true? a) There is a 0.3% chance that the mean ages for the men and women are different b) There is a 99.7% chance that another sample will give these same results c) It is very unlikely that the professor would see results like these if the mean age of men was equal to the mean age of women. d) There is a 0.3% chance that another sample will give these same results

c) It is very unlikely that the professor would see results like these if the mean age of mean was equal to the mean age of women

A researcher found that a 98% confidence interval for the mean hours per week spent studying by college students was (13, 17). Which is true? I. There is a 98% chance that the mean hours per week spent studying by college students is between 13 and 17 hours. II. 98% of college students study between 13 and 17 hours a week III. Students average between 13 and 17 hours per week studying on 98% of the weeks. a) III only b) II only c) None of the statements are true d) I only

c) None of the statements are true

A company checking the productivity of its assembly line monitored a random sample of workers for several days. They found that a 95% confidence interval for the mean number of items produced daily by each worker was (23, 27). Which is true? a) 95% of the workers sampled produced between 23 and 27 items b) 95% of all the workers average between 23 and 27 items a day c) We're 95% sure that the mean daily worker output is between 23 and 27 items d) 95% of samples would show mean production between 23 and 27 items a day

c) We're 95% sure that the mean daily worker output is between 23 and 27 items.

In an experiment, the primary purpose of blinding is to reduce what? a) Bias b) Undercoverage c) Confounding d) Variation

a) Bias

Placebos are a tool for what? a) Blinding b) Sampling c) Control d) Blocking

a) Blinding

A producer of a new diet supplement pill boasts that their product helps users lose more weight than the current leading board. They provide evidence from a double-blind placebo controlled randomized clinical trial which tested the null hypothesis H0: μ new- μ old = 0 against the alternative HA: μ new- μ old > 0 where μ represents the mean weight loss. Which of the following would be a type I error? a) Deciding that dieters on the new pill will lose more weight, when in fact they don't b) Deciding that dieters on the new pill don't lose more weight, when in fact they do c) Deciding that dieters on the new pill don't lose more weight, when in fact they don't d) Deciding that dieters on the new pill lose more weight, when in fact they do

a) Deciding that dieters on the new pill lose more weight, when in fact they don't

Trainers need to estimate the level of fat in athletes to ensure good health. Initial tests were based on a small sample but now trainers double the sample size for a follow-up test. The main purpose of the larger sample is to do what? a) Decrease the standard deviation of the sampling model b) Reduce non-response bias c) Reduce confounding due to other variables d) Decrease the variability in the population

a) Decrease the standard deviation of the sampling model

A company is developing a new high performance wax for cross country ski racing. In order to justify the price marketing wants, the wax needs to be very fast. Specifically, the mean time to finish their standard test course should be less than 55 seconds for a former Olympic champion. To test it, the champion will ski the course 8 times. Complete parts a and b below. a) The champion's times (selected at random) are 56.5, 63.9, 47.3, 51.3, 46.6, 48.1, 54.2, and 44.8 seconds to complete the test course. Should they market the wax? Assume the assumptions and conditions appropriate hypothesis testing are met for the sample. Assume α = 0.05 Choose the correct null and alternative hypothesis below. a. H0: μ> 55 HA: μ = 55 b. H0: μ = 55 HA: μ< 55 c. H0: μ < 55 HA: μ = 55 d. H0: μ= 55 HA: μ > 55 Calculate the test statistic Calculate the p-value Choose the correct conclusion below a. No, do not market the wax as there is insufficient evidence to conclude the mean time is less than 55 seconds b. Yes, market the wax as there is sufficient evidence to conclude the mean time is less than 55 seconds c. No, do not market the wax as there is sufficient evidence to conclude the mean time is less than 55 seconds d. Yes, market the wax as there is insufficient evidence to conclude the mean time is less than 55 seconds. b) Suppose they decide not to market the wax after the test, but it turns out that the wax really does lower the champion's average time to less than 55 seconds. What kind of error have they made? Explain the impact to the company of such an error. a. They have made a type II error and customers might demand their money back b. They made a type I error and will lose the potential profit from selling the wax c. They have made a type I error and customers might demand their money back. d. They have made a type II error and will lose the potential profit from selling the wax.

a) H0: μ = 55 HA: μ < 55 T = -1.515 P-value = 0.0868 a. No, do not market the wax as there is insufficient evidence to conclude the mean time is less than 55 seconds. b) d. They have made a type II error and will lose the potential profit from selling the wax.

A researcher has calculated a 95% confidence interval and would prefer for his next confidence interval to have a smaller margin of error without losing any confidence. In order to do this, which of the following can be done? I. Change the z*- value to a smaller number II. Take a larger sample III. Take a smaller sample a) II only b) I and II c) I only d) III only

a) II only

What is true about a 98% confidence interval for a population proportion based on a given sample? I. We are 98% confident that the other sample proportions will be in our interval II. There is a 98% chance that our interval contains the population proportion. III. The interval is wider than a 95% confidence interval would be a) III only b) II only c) I only d) I and II

a) III only

A researcher wants to know the mean winning score at an annual major golf tournament. An internet search gives the researcher all the scores for the history of that tournament, and the researcher creates a 95% confidence interval based on a t-distribution. This procedure was not appropriate. Why? a) The entire population of scores was gathered, so there is no reason to do inference. b) The population standard deviation is known, so the researcher should have used a z-model c) In big golf tournaments the players are not randomly selected d) Since these are the best players in the world, the scores are probably skewed

a) The entire population of scores was gathered, so there is no reason to do inference.

Bernard ran an experiment to test optimum power and time settings for microwave popcorn. His goal was to deliver popcorn fewer than 12% of the kernels left unpopped, on average. He determined that power 9 at 4 minutes was the best combination. Complete a) and b) below. a) He concluded that this popping method achieved the goal of fewer than 12% of the kernels left unpopped. If it really does not work that well, what kind of error did Bernard make? Type I error or Type II error? b) To be sure that the method was successful, he popped 8 more bags of popcorn (selected at random) at this setting. All were on high quality, with the percentages of unpopped kernels shown below 5.1, 13.7, 5.2, 12.3, 11.6, 6.5, 7.1, 4.4 Does this provide evidence that he met his goal of an average of fewer than 12% unpopped kernels? Assume α = 0.05 a. H0: μ ≠ 12 HA: μ = 12 b. H0: μ < 12 HA: μ = 12 c. H0: μ = 12 HA: μ ≠ 12 d. H0: μ > 12 HA: μ = 12 e. H0: μ = 12 HA: μ > 12 f. H0: μ = 12 HA: μ < 12 Choose the correct null and alternative hypotheses. Calculate the test statistic. Calculate the P-value Does this provide evidence that Bernard met his goal? a. No, there is not enough evidence to reject the hypothesis that 12% (or more) of the kernels were left unpopped b. Yes, there is enough evidence to reject the hypothesis that 12% (or more) of the kernels were left unpopped c. Yes, there is enough evidence to accept the hypothesis that less than 12% of the kernels were left unpopped d. No, there is not enough evidence to accept the hypothesis that less than 12% of the kernels were left unpopped

a) Type I error b) f. H0: μ = 12 HA: μ <12 T= -2.877 P-value= 0.0119 b. Yes, there is enough evidence to reject the hypothesis that 12% (or more) of the kernels were left unpopped.

Which of the following is a correct interpretation of a p-value that is not very small? a) What we saw in the sample is not surprising, so we fail to reject the null hypothesis b) We have witnessed a rare event, so we should reject the null hypothesis c) we have witnessed a rare event, so we should fail to reject the null hypothesis d) What we saw in the sample is not surprising, so we reject the null hypothesis

a) What we saw in the sample is not surprising, so we fail to reject the null hypothesis

A magazine is considering the launch of an online edition. The magazine plans to go ahead only if it is convinced that more than 30% of current readers would subscribe. The magazine contracted a simple random sample of 500 current subscribers, and 175 of those surveyed expressed interest. What should the company do? Test appropriate hypotheses and state you conclusion. a) Are the assumptions and the conditions to perform a one-proportion z-test met? Yes or No? b) State the null and alternative hypotheses. Choose the correct answer below. a. H0: p = 0.3 HA: p ≠ 0.3 b. H0: p = 0.3 HA: p < 0.3 c. H0: p = 0.3 HA: p > 0.3 d. The assumptions and conditions are not met, so the test cannot proceed c) Determine the z-test statistic. Select the correct choice below and if necessary, fill in the answer box to complete your choice. a. z = b. The assumptions and conditions are not met, so the test cannot proceed d) Find the p-value. Select the correct choice below and if necessary, fill in the answer box to complete your choice. a. P-value= b. The assumptions and conditions are not met, so the test cannot proceed e) What is your conclusion? Choose the correct answer below. a. Since the P-value was high, fail to reject H0 b. Since the P-value was low, reject H0. c. The assumptions and conditions are not met, so the test cannot proceed f) What should the company do? Choose the correct answer below. a. The survey results would be highly unusual is less than 30% of the current readers were interested. The company should not launch the online edition b. The survey results would be highly unusual if less than 30% of the current readers were interested. The company should launch the online edition c. The survey results would not be unusual if less than 30% of the current readers were interested. The company should launch the online edition. d. The assumptions and conditions are not met, so the test is not valid.

a) Yes b) c. H0: p = 0.3 HA: p > 0.3 c) a. Z = 2.44 d) a. P-value = 0.0073 e) b. Since the P-value was low, reject H0 f) b. The survey results would be highly unusual if less than 30% of the current readers were interested. The company should launch the online edition.

19. An airline's public relations department says that the airline rarely loses passengers' luggage. It further claims that on those occasions when luggage is lost, 93% is recovered and delivered to its owner within 24 hours. A consumer group who surveyed a large number of air travelers found that only 99 of 199 people who lost luggage on that airline were reunited with the missing items by the next day. Does this cast doubt on the airline's claim? Explain. a) Are the assumptions and the conditions to perform a one-proportion z-test met? Yes or No? b) State the null and alternative hypotheses. Choose the correct answer below. a. H0: p= 0.93 HA: p> 0.93 b. H0: p= 0.93 HA: p≠ 0.93 c. H0: p= 0.93 HA: p< 0.93 d. The assumptions and conditions are not met, so the test cannot proceed c) Determine the z-test statistic. Select the correct choice below and if necessary, fill in the answer box to complete your choice a. z= b. The assumptions and conditions are not met, so the test cannot proceed d) Find the p-value. Select the correct choice below and if necessary, fill in the answer box to complete your choice. a. P-value= b. The assumptions and conditions are not met, so the test cannot proceed e) Do the results of the survey cast doubt on the airline's claim? Explain. Choose the correct answer below. a. No, since the null hypothesis is rejected b. Yes, since the null hypothesis is not rejected c. Yes, since the null hypothesis is not rejected d. Yes, since the null hypothesis is rejected e. The assumptions and conditions are not met, so the test cannot proceed

a) Yes b) c. H0: p = 0.93 HA: p < 0.93 c) a. Z = -23.91 d) a. P-value = 0 e) d. Yes, since the null hypothesis is rejected.

Some people claim they get relief from stiff joints by drinking a large glass of ice cold lemonade. Researchers plan to enlist several people who suffer from stiff joints in a test. When a participant experiences stiff joints, he or she will take a pill that may be a standard pain reliever or a placebo. Half of each group will also drink ice cold lemonade. Each participant has an equal chance of receiving any treatment. Complete parts a) - d) below. a) Identify the factors and levels in the experiment. Select all that apply. a. Beverage ( none or ice cold lemonade) b. Intensity of stiff joints (Mild, moderate, severe) c. Frequency of stiff joints (daily, weekly, or monthly) d. Pain Reliever (standard or placebo) b) Identify the number of treatments and the response variable Identify the response variable measured. Choose the correct answer below. a. Body Temperature b. Amount of cold lemonade consumed c. Level of pain relief c) Is there any blinding described in the study? Choose the correct answer below. a. Double-blind in regard to type of pain reliever and beverage b. Single-blind in regard to type of pain reliever c. Double-blind in regard to type of beverage d. No blinding d) No blocking is described in the study. What might be an appropriate variable on which to block? Clearly explain why you think this variable would be appropriate. Which variables could be used to block? Select all that apply. a. Gender b. Intensity of stiff joints c. Age d. Occupation e. Frequency of stiff joints f. Amount of cold lemonade consumed Why would this/these variables be appropriate variables on which to block? Choose the correct answer below. a. There is reason to think that this/these variables affect the blinding of the study b. There is reason to think that this/these variables affect the response variable c. There is reason to think that this/these variables affect the factors d. There is reason to think that this/these variables affect the treatments

a) a. and d. Beverage (none or ice cold lemonade) Pain Reliever (standard or placebo) b) There are 4 treatments c. Level of pain relief. c) b. Single- blind in regard to type of pain reliever. d) a. Gender, c. Age, e. Frequency of stiff joints, b. Intensity of stiff joints There is reason to think that this/these variables affect the response variable.

Data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. The data set also notes for each town whether it was south or north of the derby. The summary statistics are given below. Is there a significant difference in mortality rate s in the two regions? Answer parts a and b. Assume a significance level of 0.05. a) Test the null hypothesis at α= 0.05 using the two-sample t-test a. H0: μ N - μ S = 0 HA: μ N - μ S < 0 b. H0: μ N - μ S ≠ 0 HA: μ N - μ S = 0 c. H0: μ N - μ S = 0 HA: μ N - μ S > 0 d. H0: μ N - μ S = 0 HA: μ N - μ S ≠ 0 Identify the null and alternative hypotheses. Choose the correct answer below. Complete a t-statistic Find the P-value State the conclusion. Recall that α= 0.05. a. Reject H0. There is not sufficient evidence that the mean mortality rate is different for the two towns b. Fail to reject H0. There is sufficient evidence that the mean mortality rate is different for the two towns c. Reject H0. There is sufficient evidence that the mean mortality rate is different for the two towns d. Fail to reject H0. There is not sufficient evidence that the mean mortality rate is different for the two towns Choose the correct answer below. b) The boxplots of the two distributions show an outlier among the data north of the Derby. What effect might that have had on the test? Choose the correct answer below. a. Since only one sample has an outlier, the results are still valid b. The effect of the outlier will be so small, so the results are still valid c. The outlier does not affect any of the summary data, so the results are valid d. The outlier means that the data may not be normal, so the results are not valid.

a) d. H0: μ N - μ S = 0 HA: μ N- μ S ≠ 0 T= 0.519 The p-value is 0.6057 d. Fail to reject H0. There is not sufficient evidence that the mean mortality rate is different for the two towns b) d. The outlier means that the data may not be normal, so the results are not valid.

A researcher is about to test a hypothesis using data from a well-designed study. Which is true? I. A large p-value would be strong evidence against the null hypothesis II. The researcher can set a higher standard of proof by choosing α= 10% instead of 5%. III. If the researcher reduces the risk of committing a type I error, then the risk of a type II error will also decrease. a) None of the statements are true b) II only c) I only d) III only

a) none of the statements are true.

In a certain running event, preliminary heats are determined by random draw, so it would be expected that the abilities of runners in the various heats are about the same, on average. The accompanying table shows the times (in seconds) for preliminary heats 2 and 5 in a particular year. Is there any evidence that the mean time to finish is different for randomized heats? Explain. Be sure to include a discussion of assumptions and conditions for the analysis. a) Discuss the assumptions and conditions for the analysis. Select all that apply. b) Before continuing with the hypothesis testing, eliminate any outliers in the sample data. Conduct a hypothesis test to test whether the mean time to finish is differenct for randomized heats. Note that μ2 and μ5 are the population means for heat 2 and heat 5, respectively. Identify the null and alternative hypothesis. Choose the correct answer below. a. H0: μ 2 - μ 5 ≠ 0 HA: μ 2 - μ 5 = 0 b. H0: μ 2 - μ 5 = 0 HA: μ 2 - μ 5 > 0 c. H0: μ 2 - μ 5 = 0 HA: μ 2 - μ 5 ≠ 0 d. H0: μ 2 - μ 5 =0 HA: μ 2 - μ 5 < 0 c) Determine the t-statistic, t. d) Determine the P-value. e) State the conclusion. Use a significance level of 0.05 to draw the conclusion

a)The Nearly Normal Condition is violated. b) c. H0: μ 2 - μ 5= 0, HA: μ 2 - μ 5 ≠ 0 c)T = -0.24 d)P-value = 0.815 e)Do not reject the null hypothesis. There is not sufficient evidence to support the claim that the mean running times in heat 2 and heat 5 are different.

There is some concern that is women over age 64 who take supplemental hormones also drink alcohol, their hormones levels will drop too low. Eighteen volunteers on hormone therapy were randomly divided into two groups, as were 19 other volunteers not on hormone therapy. In each case, one group drank an alcoholic beverage, the other a nonalcoholic beverage. An hour later everyone's hormone level was checked. Only those on supplemental hormones who drank alcohol showed a marked decrease. a) Identify whether the above research is an observational study or an experiment. The described research is an... b) Identify the subjects studied The subjects were.... c) Identify the factors in this experiment, and the number of levels for each How many factors are involved in this experiment? Name the factor: Number of levels: d) Identify the number of treatments This experiment used ... e) Identify the response variable measured The response variable is .. f) Identify the design (completely randomized, blocked, or matched) This experiment has a g) Identify whether the experiment was blind (or double blind) a. this experiment is single-blind. The subjects were blinded b. This experiment is double-blind c. This experiment is single-blind. The evaluators were blinded. d. It is not known whether any blinding occurred h) Identify the nature and scope of the conclusion regarding what the results of the experiment may or may not indicate. a. This experiment indicates that drinking alcohol leads to dangerous hormone levels among those taking hormone supplements b. The experiment indicates that women over 64 who take hormone supplements should drink alcohol. c. This experiment indicates that taking hormone supplements leads to decreased hormone levels among those drinking alcohol d. This experiment indicates that drinking alcohol leads to decreased hormone levels among those taking hormone supplements.

a)The described research is an Experiment b)The subjects were 37 women over 64 c)Factors involved: 1 Name the factor: Type of Drink Number of levels: 2 d) This experiment used 2 treatments e) The response variable is Hormone Level f) This experiment has a Randomized Block design g) d. It is not known whether any blinding occurred h) d. This experiment indicates that drinking alcohol leads to decreased hormone levels among those taking hormone supplements

A survey asked people "On what percent of days do you get more than 30 minutes of vigorous exercise?" Using their responses, a researcher wants to estimate the difference in exercise frequency between men and women. What should the researcher use? a) 1-sample t-interval b) 2-sample t-interval c) Matched pairs t-interval d) 1-proportion z-interval

b) 2-sample t-interval

Which of the following is not required in an experimental design? a) Control b) Blocking c) Replication d) Randomization

b) Blocking

A statistics professor wants to see if more than 80% of her students enjoyed taking her class. At the end of the term, she takes a random sample of students from her large class and asks, in an anonymous survey, if the students enjoyed taking her class. Which set of hypotheses should she test? a) H0: p > 0.80 HA: p = 0.80 b) H0: p = 0.80 HA: p > 0.80 c) H0: p < 0.80 HA: p > 0.80 d) H0: p = 0.80 HA: p < 0.80

b) H0: p = 0.80 HA: p > 0.80

Why is double blinding in experiments important? I. The elevators should not know which treatment group the participants are in. II. The participants should not know which treatment group they are in III. No one should know which treatment any of the participants are getting. a) III only b) I and II c) II only d) I only

b) I and II

A researcher is about to test a hypothesis using data from a well-deigned study. Which is true? I. A small p-value would be strong evidence against the null hypothesis. II. The researcher can set a higher standard of proof by choosing α = 10% instead of 5% III. If the researcher reduces the alpha level, the researcher reduces the power of the test. a) III only b) I and III only c) II only d) I only

b) I and III only

Investigators at an agricultural research facility randomly assigned equal numbers of chickens to be housed in two rooms. In one room a group of chickens experienced normal day/night cycles, while in the other room lights were left on 24 hours a day to see if those chickens would lay more eggs. After collecting data for several days the researchers tested the hypothesis H0: μ 1 - μ 2 = 0 against the one-tail alternative and found P= 0.22. Which is true? a) There's a 22% chance that chickens housed in a lighted room produce more eggs b) None of these c) The chickens in the lighted room averaged 0.22 more eggs a day d) There's a 22% chance another experiment will give these same results

b) None of these

Of the following, which is not a critical part of designing a good experiment? a) Replication of a sufficient number of subjects b) Random selection of subjects c) Random assignment of subjects to treatments d) Control of known sources of variability

b) Random selection of subjects

Suppose that a manufacturer is testing one of the machines to make sure that the machine is producing more than 97% good parts (H0: p = 0.97 and HA: p > 0.97). The test results in a p-value of 0.122. Unknown to the manufacturer, the machine is actually producing 99% good parts. What probably happens as a result of the testing? a) They fail to reject H0, making a type I error b) They fail to reject H0, making a type II error c) They correctly fail to reject H0 d) They correctly reject H0

b) They fail to reject H0, making a type II error.

Absorption rates into the body are important when manufacturing a generic version of a brand-name drug. A Pharmacist read that the absorption rate into the body of a new generic drug (G) is the same as its brand-name counterpart (B). She has a researcher friend of hers run a small experiment to test H0: μ G- μ B ≠ 0. Which of the following would be a type I error? a) Deciding that the absorption rates are the same, when in fact they are b) Deciding that the absorption rates are different, when in fact that are c) Deciding that the absorption rates are the same, when in fact they are not d) Deciding that the absorption rates are different, when in fact they are not

d) Deciding that the absorption rates are different, when in fact they are not.

A contact lens wearer read that the producer of a new contact lens boasts that their lenses are cheaper than contact lenses from another popular company. She collected some data, then tested the null hypothesis H0: μ old - μ new > 0. Which of the following would be a type II error? a) Deciding that the new lenses are cheaper, when in fact they really are b) Deciding that the new lenses are cheaper, when in fact they are not. c) Deciding that the new lenses are not really cheaper, when in fact they are not d) Deciding that the new lenses are not really cheaper, when in fact they are.

d) Deciding that the new lenses are not really cheaper, when in fact they are.

Company executives wish to estimate the dollar amount that customers spend in one shopping visit to their store. Initial tests were based on a small sample but now the executives double the sample size for a follow-up test. The main purpose of the larger sample is to do what? a) Reduce confounding variable due to other variables b) Reduce response bias c) Decrease the variability in the population d) Decrease the standard deviation of the sampling model

d) Decrease the standard deviation of the sampling model.

Which statement correctly compares t-distributions to the normal distribution? I. T-distributions are also mound shaped and symmetric II. T-distributions are more spread out than the normal distribution III. As degrees of freedom increase, the variance of t-distributions becomes larger. a) I and III only b) II only c) I only d) I and II only

d) I and II only

Which of the statements correctly compares t-distributions to the Normal distribution? I. t-distributions are also mound shaped and symmetric II. t-distributions have less spread than the normal distribution III. As degrees of freedom increase, the variance of t-distributions becomes smaller. a) I and II only b) II only c) I only d) I and III only

d) I and III only

Not wanting to risk poor sales for a new soda flavor, a company decides to run one more taste test on potential customers, this time requiring a higher approval rating than they had for earlier tests. What will this higher standard of proof increase? I. The risk of type I error II. The risk of type II error III. Power a) I and II b) I only c) III only d) II only

d) II only

Which is true about a 95% confidence interval based on a given sample? I. The interval contains 95% of the population II. Results from 95% of all samples will lie in the interval. III. The interval is narrower than a 98% confidence interval would be. a) I only b) II and III only c) II only d) III only

d) III only

A researcher investigating whether joggers are less likely to get colds than people who do not jog found a p-value of 3%. What does this mean? a) Joggers get 3% fewer colds than non-joggers b) There's a 3% chance that joggers get fewer colds c) There's a 3% chance that joggers don't get fewer colds d) None of the above

d) None of the above

A pharmaceutical company investigating whether drug stores are less likely than food stores to remove over-the-counter drugs from the shelves when the drugs are past the expiration date found a P-value of 2.8%. What does this mean? a) There is a (7.2% chance the drug stores remove more expired over-the-counter drugs b) 97.2% more drug stores remove over-the-counter drugs from the shelves when the drugs are past the expiration date than food stores c. 2.8% more drug stores remove over-the-counter drugs from the shelves when the drugs are past the expiration date. d) None of these

d) None of these

An old myth claims that boys are better at math than girls. A high school guidance counselor collects the math grades from a random sample of 50 boys and another random sample from 50 girls. The guidance counselor then tested the hypothesis H0 = μ1 - μ2= 0 against the one-tail alternative and found P = 0.35. Which is true? a) The boys' grades are 35% higher than the girls' grades b) There's a 35% chance that there 's really no difference in math grades c) There's a 35% chance that boys have higher math grades than girls d) None of these

d) None of these

What does a p-value indicate? a) The probability that the null hypothesis is true, given the observed statistic b) The probability that the null hypothesis is true c) The probability of the observed statistic, given that the alternative hypothesis is true d) The probability of the observed statistic, given that the null hypothesis is true.

d) The probability of the observed statistic, given that the null hypothesis is true.

To plan the course offerings for the next year a university department dean needs to estimate what impact the "No child left behind" legislation might have on the teacher credentialing program. Historically, 40% of this university's pre-service teachers have qualified for paid internship positions each year. The dean of education looks at a random sample of the internship applications to see what proportion indicate the applicant has achieved the content-mastery that is required for the internship. Based on these data he creates a 90% confidence interval of (33%, 41%). Could this confidence interval be used to test the hypothesis H0: p = 0.40 versus HA: p < 0.40 at the α = 0.05 level of significance? a) Yes, since 40% is not the center of the confidence interval he rejects the null hypothesis, concluding that the percentage of qualified applicants will decrease. b) Yes, since 40% is in the confidence interval he accepts the null hypothesis, concluding that the percentage of applicants qualified for paid internship positions will stay the same. c) No, because the dean should have used a 95% confidence interval d) Yes, since 40% is in the confidence interval he fails to reject the null hypothesis, concluding that there is not strong enough evidence of any change in the percent of qualified applicants.

d) Yes, since 40% is in the confidence interval he fails to reject the null hypothesis, concluding that there is not strong enough evidence of any change in the percent of qualified applicants.