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Students in an online course are each randomly assigned to receive either standard practice exercises or adaptive practice exercises. For the adaptive practice exercises, the next question asked is determined by whether the student got the previous question correct. The teacher of the course wants to determine whether there is a difference between the two practice exercise types by comparing the proportion of students who pass the course from each group. The teacher plans to test the null hypothesis $$p_S = p_A$$ that versus the alternative hypothesis $$p_S \neq p_A$$, where $$p_S$$ represents the proportion of students who would pass the course using standard practice exercises and $$p_A$$ represents the proportion of students who would pass the course using adaptive practice exercises. The teacher knows that the 99 percent confidence interval for the difference in proportion of students passing the course for the two practice exercise types (standard minus adaptive) is (0.03, 0.24) and the 90 percent confidence interval for the difference in the proportion of students passing the course for the two practice exercise types (standard minus adaptive) is (0.06, 0.21). Which of the following is the most reasonable conclusion for the teacher's hypothesis test at the $$\alpha = 0.05$$ level?

An experiment was conducted to assess the effect of baking temperature on the density of bread. A large batch of white bread dough and a large batch of whole wheat bread dough were prepared. Each of the batches was formed into 18 loaves, resulting in a total of 36 loaves. Each of the white bread loaves was randomly assigned to one of three baking temperatures (low, medium, and high), so that 6 loaves were baked at the low temperature, 6 were baked at the medium temperature, and 6 were baked at the high temperature. A similar process of random assignment was carried out for the whole wheat bread loaves. Which of the following are the treatments in the experiment?

Concerned about the length of high school basketball games, the governing body for high school sports in a certain state is investigating the possibility of shortening game length if the mean game length is greater than 90 minutes. A random sample of 25 games from the current season was selected, and the sample mean game length was 95 minutes with a sample standard deviation of 10 minutes. Assuming that the distribution of game length is approximately normal, which of the following is the appropriate probability statement for determining the $$p$$-value of the hypothesis test to investigate whether the mean game length is greater than 90 minutes?

A chocolatier, a person who makes chocolate candy, at a candy company has developed a new dark chocolate candy and believes it will be less bitter than the current dark chocolate candy on the market. The chocolatier hired 40 professional taste testers to participate in an experiment. The chocolatier flipped a coin for each participant. If the coin landed on heads, the participant tasted the new dark chocolate candy first, then tasted the current dark chocolate candy. If the coin landed on tails, the participant tasted the current dark chocolate candy first, then tasted the new dark chocolate candy. The participants rated the bitterness of each dark chocolate candy on a scale of 1 to 10, with 1 being the least bitter and 10 being the most bitter. Using a paired $$t$$-test to test the belief, the chocolatier calculated a $$p$$-value of 0.274. Assuming the conditions for inference have been met, which of the following is the best conclusion for the chocolatier's hypothesis test?

A public health analyst is interested in investigating whether there is a linear relationship between body mass index (BMI) and fasting blood glucose (FBG) for a particular population of adults. The analyst measured the MBI and FBG for each adult in a sample of 227 volunteers. The computer output for the linear regression analysis predicting FBG from BMI is shown.

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Assume the conditions for inference have been met. Based on the computer output, which of the following conclusions is appropriate for all adults in the population similar to those who volunteered for the study?

The distribution of body temperature for healthy adults is approximately normal with mean 98.2°F and standard deviation 0.7°F. Based on the description of the distribution, which of the following statements CANNOT be supported?

A research scientist is conducting an experiment to determine whether a new chemical process creates less toxic byproduct compared to the current chemical process. The scientist took a random sample of products made with the current chemical process and calculated the sample mean amount of toxic byproduct created. The scientist then took a random sample of products made with the new chemical process and calculated the sample mean amount of toxic byproduct created. The difference in the sample means (current minus new) was 2.31 liters of toxic byproduct. A hypothesis test was conducted using the following hypotheses.
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Assuming the conditions for inference were met, the scientist calculated the $$p$$-value of the test to be 0.072. Which of the following statements is the best interpretation of the $$p$$-value?

Consider a population consisting of four children with ages, in years, of 2, 5, 6, and 11. The population mean age is 6 years, and the population variance is 10.5 square years. For simple random samples of size 2 taken with replacement, what are the mean and standard deviation of the sampling distribution of the sample mean age, in years?

For a chi-square test for independence with 6 degrees of freedom and a significance level of 0.05, the value of the test statistic was $$\chi^2 = 10.497$$. The associated $$p$$-value was 0.1052. Assuming all necessary conditions for the chi-square test were met, what type of error is possible?

A prize game at a circus has a spinner with 12 sections, where each section is equally likely to be selected when the spinner is spun. There are 7 blue sections and 5 orange sections. Camille has spun the spinner 4 times and the pattern of outcomes was orange, blue, orange, blue. Camille will spin the spinner two more times. Which of the following statements is true?

Suppose a new regulation requires businesses to pay all employees a minimum wage of ＄15.00 per hour. A small coffee shop currently has 9 employees—5 employees whose wages are less than ＄15.00 per hour and 4 employees whose wages are more than ＄15.00 per hour. To meet the new regulation, the coffee shop plans to increase the wages of the 5 employees whose wages are less than ＄15.00 per hour to ＄15.00 per hour. The other 4 employees will not receive a wage increase at this time.
Which of the following must be true about the median wage of the 9 employees after the wage increase occurs?

A technology company has 1,200 employees. The director of human resources at the company selects 250 of the employees at random, without replacement, and asks them to fill out an anonymous survey asking whether they plan to attend the company's holiday party. The proportion of employees in the sample who plan to attend the party is 0.816. Based on this proportion, the director calculates a 95 percent confidence interval for the proportion of all employees who plan to attend the holiday party as $$0.816 \pm 1.96\sqrt{\frac{(0.816)(1 - 0.816)}{250}}$$. Which of the following is true concerning whether it is appropriate to use the confidence interval to estimate the proportion of all employees who plan to attend the holiday party?

A total of 13 distinct groups, but with each group similar to the other groups, participated in a craft fair. To investigate how satisfied the participants were with the fair, the fair director conducted a survey. The director randomly selected 5 of the groups participating in the fair and surveyed all members of the selected groups. Which statement best describes the sampling method used by the director?

A grocery store received three shipments of bags of cranberries: one from farm A, one from farm B, and one from farm C. The distributions of the weight of a bag are unimodal and symmetric for all three shipments. The number of bags and the mean and standard deviation, in ounces (), for each shipment are shown in the table.

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Which of the following statements is true?

A certain computer chip company has a machine that makes a large number of computer chips. Of the computer chips produced on this machine, 3% are defective. Miriam, the quality control inspector, will randomly select computer chips from the machine to inspect. What is the probability that the first defective computer chip Miriam finds is the sixth computer chip she inspects from the machine?

A county manager selected a random sample of 200 residents from a suburban area of the county and a separate random sample of 200 residents from an urban area of the same county. The residents in the samples were asked whether they thought the county should create dog parks where residents can take their dogs to play. From those who were sampled, 41 percent of the suburban residents and 35 percent of the urban residents thought the county should create dog parks.
Let $$p_S$$ represent the population proportion of suburban residents who think the county should create dog parks, and let $$p_U$$ represent the population proportion of urban residents who think the county should create dog parks. The county manager will test the following hypotheses.
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Assuming the conditions for inference were met, which of the following is closest to the $$p$$-value of the county manager's test?

A fair coin will be tossed three times. The set of possible outcomes may be described by the ordered triples

$$\{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$$

, where $$H$$ represents heads and $$T$$ represents tails.
What is the probability that all three tosses result in heads, given that the three tosses result in more heads than tails?

A researcher wants to examine the effect of 2 different strengths—low and high—of fertilizer on the growth of corn. A field will be divided into 54 equally sized plots of land, and the 2 fertilizer strengths will be randomly assigned so that 27 plots will be fertilized with low strength and 27 plots with high strength. The same type and amount of corn will be planted in each plot at the same time. The yield (amount of corn produced) will be measured for each plot. Which of the following would provide the best evidence that the strength of fertilizer had an effect on the yield?

According to the United States Social Security Administration (SSA), for children born years ago, the following table gives the percentage of children with a first name beginning with the letters A-C, D-J, K-M, and N-Z.

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Daphne, a senior at a large high school, will investigate whether the distribution of the beginning letter of first names of students at her high school who were born 18 years ago is consistent with the percentages from the Social Security Administration. She took a random sample of 80 students from her school who were born 18 years ago. Daphne recorded the number of students with a first name beginning with the letters A-C, D-J, K-M, and N-Z. The results are shown in the following table.

（含图）
Assuming the conditions for inference are met, what is the appropriate chi-square test and calculation of the test statistic for her investigation?

To determine whether an herbal supplement helps relieve knee pain, researchers will select 50 patients with knee pain to participate in a study. The participants will be randomly assigned to one of two groups, with 25 participants in each group. The first group will receive the herbal supplement daily for one week, and the second group will receive a placebo daily for one week. Patients will continue to take their current pain medication during the week. At the end of the week, the patients will record their pain score on a scale of 1 to 10, where 1 represents no pain and 10 represents extreme pain. Assuming the conditions for inference are met, which of the following would be the most appropriate statistical method to estimate the difference in mean pain score between the herbal supplement and the placebo for all patients with knee pain who are similar to the participants in the study?

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