Sarah believes that completely cutting caffeine out of a person's diet will allow him or her more restful sleep at night. In fact, she believes that, on average, adults will have more than two additional nights of restful sleep in a four-week period after removing caffeine from their diets. She randomly selects 8 adults to help her test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days, and then cut back to no caffeinated beverages for the following 28 days. During each period, the participants record the numbers of nights of restful sleep that they had. The following table gives the results of the study. Test Sarah's claim at the 0.05 level of significance assuming that the population distribution of the paired differences is approximately normal. Let the period before removing caffeine be Population 1 and let the period after removing caffeine be Population 2. Numbers of Nights of Restful Sleep in a Four-Week Period With Caffeine 24 22 24 20 23 21 16 20 Without Caffeine 28 27 24 25 25 21 21 21 Copy Data Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.

On a particular night, a baseball stadium sells 60% of its seats, and of those, 15% do not end up showing up to the game.  Assuming everyone present is sitting in a seat, what percentage of seats in the stadium are empty?

not A 1995 study by the School of Public Health reported that 87% of male students who live in a fraterity house are binge drinkers. The figure for fraternity members who are residents of a fraternity house is 71 %, while the figure for men who do not belong to a fraternity is 44 % Suppose that 11% of U.S. male students live in a fraternity house, 15% belong to a fraterity but do not live in a fraterity house, and 74% do not belong to a fraterity a. What is the probability that a randomly selected malp student is a binge drinker? b. If a randomly selected male student is a binge drinker, what is the probability that he lives in a fraterity house? The probability that a randomly selected male student is a binge drinker is 0.5509 (Type an integer or a decimal rounded to two decimal places as needed) CETTE

A survey looked at how long it takes a typical company to recoup an investment in research. The survey determined that 39% of the corporations took six months or less to recoup their investment. The data table below shows a sample of the time, in months, it might have taken 20 corporations to recoup their investment. Complete parts a and b. 9.0 8.0 4.0 4.0 7.0 8.0 7.0 7.0 9.5 5.5 7.5 12.0 8.5 5.5 10.5 10.0 7.5 4.5 7.0 7.5 a. Determine the number of corporations that recovered their investement in research in six months or less. There were 5 corporations that recovered their investment in research in six months or less. b. Calculate the probability of obtaining at most the number of corporations that you determined in part a if the percent of those recovering their investment is as indicated by the survey. The probability (Round to four decimal places as needed.)

A medical study is conducted to determine which migraine treatment, A or B, provides faster relief. The study uses 10 volunteers who claim to suffer from migraines. Half of the volunteers are randomly assigned to use treatment A when they experience their first migraine. The other half are assigned to use treatment B. Then, after no treatment for one month, the treatments are reversed. The volunteers each record the amount of time it takes, in minutes, to experience relief from their migraine under each treatment. The data are displayed in the table. A 3-column table with 10 rows. Column 1 is labeled volunteer with entries 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Column 2 is labeled Treatment A with entries 10, 13, 13, 9, 13, 12, 14, 10, 8, 7. Column 3 is labeled Treatment B with entries 19, 18, 19, 15, 20, 16, 16, 16, 13, 17. A 99% confidence interval for the mean difference (A – B) in the time it takes to experience relief is –8.37 minutes to 0.732 minutes. Based on the confidence interval,…

In a study of exhaust emissions from school buses, the pollution intake by passengers was determined for a sample of nine school buses used in the Southern California Air Basin. The pollution intake is the amount of exhaust emissions, in grams per person per million grams emitted, that would be inhaled while traveling on the bus during its usual 18-mile18-mile trip on congested freeways from South Central LA to a magnet school in West LA. (In comparison, a city of 11 million people will inhale a total of about 1212 grams of exhaust per million grams emitted.) The amounts for the nine buses when driven with the windows open are given in the table. 1.15 0.33 0.40 0.33 1.35 0.38 0.25 0.40 0.35   A good way to judge the effect of outliers is to do your analysis twice, once with the outliers and a second time without them. Give the 90%90% confidence interval with all the data for the mean pollution intake among all school buses used in the Southern California Air Basin that…

An interdepartmental task force is being formed to investigate an increase in violent crimes. 1/5 of the task force will be police officers from the local precinct. 1/4 will be ATF agents, and the remaining 22 will be from the FBI. How many people are participating in the task force?

Many golfers wear wrist bracelets containing magnets because they claim the magnets improve balance and the length of shots played off the tee. A golfer would like to determine if the claim has merit and finds 200 volunteers who play golf to participate in an experiment. Half of the golfers are randomly assigned to wear a bracelet with magnets, while the other half wear a bracelet without magnets.  Each golfer plays normally for a month, after which the length of their shots in a subsequent round is recorded. What is the response variable in this experiment? the age of each golfer the 200 volunteers the length of shots played by the golfers whether the golfers wear or do not wear the bracelet

Mateo believes that completely cutting caffeine out of a person's diet will allow them more restful sleep at night. He randomly selects 8 adults to help him test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days and then cut back to no caffeinated bevarages for an additional 28 days. During each period, the participants record the number of nights of restful sleep that they had. The following table gives the results of the study. Test Mateo's claim at the 0.05 level of significance. Give answers to 4 decimal places as needed. Number of Nights of Restful Sleep in a Four-Week Period 15 With Caffeine 21 20 22 24 18 21 24 20 26 26 22 21 23 27 23 Without Caffeine a) The normal probability plot showed the differences follow a normal distribution and the boxplot showed no outliers. b) Test the claim (1) Determine the null and alternative hypotheses. Enter correct symbol and values Ho: H₁: (2) Type of test: (3) a = (4) Test statistic (to) = p-value =…

An aerosolized vaccine for measles was developed in Mexico and has been used on 44 million children since 1980. Aerosolized vaccines have the advantages of being able to be administered by people without clinical training and do not cause injection‐associated infections. The percentage of children developing an immune response to measles after receiving the subcutaneous injection of the vaccine is 95%,95%, and for those receiving the aerosolized vaccine, it is 85%85% . There are 2020 children to be vaccinated for measles using the aerosolized vaccine in a small rural village in India. We are going to count the number who developed an immune response to measles after the vaccination.   (b) What is the probability that at least one child does not develop an immune response to measles after receiving the aerosolized vaccine? (Enter your answer as a proportion rounded to four decimal places.)