10 questions

23 minutes

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1. Players in the National Football League weigh, on average, about 248 pounds with a standard deviation of about 47 pounds. If four players are to be selected at random, the expected value of the random variable W, the total combined weight of the four players, is 992 pounds. The standard deviation of Wis approximately

2. When a patient complains to the doctor about a certain set of symptoms, the doctor diagnoses the patient with Condition A 15% of the time. If a patient with these symptoms is diagnosed with Condition A, he or she is diagnosed with Condition B 70% of the time. A patient with these symptoms that is not diagnosed with Condition A is diagnosed with Condition B 10% of the time. What is the probability that a patient with this set of symptoms will be diagnosed with at least one of these conditions?

3. A doctor hopes that a new surgery technique will shorten the recovery time compared to the standard technique. To test this, he designed an experiment in which patients who required this type of surgery were randomly assigned to the standard technique or the new technique. Then the mean recovery time for each treatment group was compared. Assuming conditions for inference were met, which analysis should be used?

4. For a class project, a student wants to see if boys and girls at their large high school differ in the number of contacts they have stored in their phone. The student conducts a survey of 50 randomly sampled boys and 40 randomly selected girls, and asks them to report the number of contacts. Which of the following is true about this situation?

5. Which of these is the best description of a P-value?

6. A farmer who raises hens for egg production wants his eggs to have a mean mass of 56 grams. He is considering the purchase of a different type of hen, so he took a random sample of 18 eggs laid by this type of hen. The distribution of the masses is symmetric and mound-shaped with a mean of 54.1 grams and no outliers. The farmer conducted a t-test to see if there is evidence that the eggs from these hens have a mean mass that is different from 56 g and got a test statistic of t= -1.973. If he uses a 5% significance level, which is the correct conclusion and reason?

7. An experiment is conducted in which the response variable is the average gain in participants' performance in the long jump. A two-sample t-test with a 5% level of significance will be used to analyze the results. If all else is kept the same, which of the following descriptions of a possible change in procedure is true?

8. Researchers wish to test how rangelands growth is affected by wildfire. A very large open area is divided into 28 equally sized plots and subjected to a controlled burn. One year later, the researchers calculate the percentage of grass returned in each plot after the fire damage. The average percentage return for these 28 plots was 58.5% with a standard deviation of 6.5%. Which of the following represents a 95% confidence interval to estimate the average proportion of grass return one year after a fire?

9. Which of the following is NOT true of the χ^{2}probability distribution function?

10. Tucson, Arizona, hosts the world's largest gem and mineral show every February. A government official claims that more than 50% of city residents have been to the Gem Show at least once. You decide to test this theory, take a simple random sample of 200 Tucson residents, and discover that 108 have attended. Which of the following is the appropriate calculation of the test statistic for the hypothesis proposed by the government official?