The hatcheck staff has had a long day, and at the end of the party they decide to return people’s hats at random. Suppose that npeople have their hats returned at random. We previously showed that the expected number of people who get their own hat back is 1, irrespective of the total number of people. In this problem we will calculate the variance in the number of people who get their hat back.Let Xi= 1if the ith person gets his or her own hat back and 0 otherwise. Let Sn::= n i=1 Xi, so Snis the total number of people who get their own hat back. Show that (a) E [Xi2] = 1/n.

Suppose that the blood pressure for a randomly selected patient has an average of 22 and variance of 441. If a sample of 220 patients is selected, then what is P(-1.2 < X< 1.4) ?

A researcher wanted to find the effect of a special diet on systolic blood pressure. She selected a sample of seven adults and put them on this dietary plan for 3 months. The following table gives the systolic blood pressures (in mm Hg) of these seven adults before and after the com- pletion of this plan. Before After 210 193 180 186 195 186 220 223 231 220 199 183 224 233 Let u be the mean reduction in the systolic blood pressures due to this special dietary plan for the population of all adults. Construct a 95% confidence interval for ud. Assume that the population of paired differences is (approximately) normally distributed.

A transect is an archaeological study area that is  mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance . In a different section of Chaco Canyon, a random sample of 23 transects gave a sample variance  for the number of sites per transect. Use an  to test the claim that the variance in the new section is greater than 36.4.​ What is the level of significance?   90%   1%   5%   95%   10%

A doctor wants to determine if a new medication for cholesterol is more effective than the previous medication. The doctor asks her patients if they would like to take part in a study for a new medication, and 30 patients currently taking medication for cholesterol volunteer to participate. Which of the following would be an appropriate procedure for this experiment? The doctor needs to randomly assign 15 patients to the new medication and 15 to the original medication to even out the variability between the patients. The doctor needs to assign the first 15 patients to the new medication and 15 to the original medication to even out the variability between patients. The doctor needs to let the 30 patients choose which medication they are going to take through use of a survey to determine whether they want to participate in the experiment. The doctor needs to randomly assign the 30 patients to the new medication to even out the variability between the patients and to determine if…

An experiment where a patient's blood pressure is measured before a treatment (call it X;) and after the treatment (call it Y;). The difference in the blood pressue of each patient, Z; = Y; – X; is also recorded. The sample size n of patients is large. Suppose the true population mean of the patient's blood pressure before treatment is 41 and after treatment is 42, both unknown. Suppose the true population variance of the patient's blood pressue before and after treatment are the same, but unknown. Find an approximate 1-a confidence interval for 12 - 41- 2.

Suppose the average height of all humans is normally distributed with a mean of 72 inches and a variance of 18 inches. Use this information to answer the following three questions. 1. Determine P(75<x<84). 2. Determine P(x>80). 3. Determine P(x < 65).

Suppose that Mary, Gary, and Larry have been asked to randomly sample 100 patients' visit records from a file of 2000 patient records and record the amount of time the attending physician spent with each patient. Gary suggests the time of year during which the patient was seen may be a confounding variable and strongly advises dividing the year into quarters (Jan - Mar, Apr-Jun, Jul-Sep, Oct- Dec) and randomly selecting 25 patient records from each quarter. Which of the following best describes Gary's sampling plan? (A) A simple random sample (B) A systematic random sample (C) A stratified random sample (D) A cluster sample (E) A convenience sample