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- A researcher examines whether an over-the-counter cold medication influences mental alertness of prison wardens. A random sample of n = 16 participants is obtained, and each person is given a standard dose of the medication one hour before being tested on a simulation task. For the general population, scores on the simulation task are
normally distributed with µ = 60 and σ = 8. The individuals in the sample had an average score of M = 56.
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- A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.34. A dietician is asked to test this claim and finds that a random sample of 16 servings has a variance of 1.22. At α=0.05, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below.Researchers interested in lead exposure due to car exhaust sampled the blood of 52 police officers subjected to constant inhalation of automobile exhaust fumes while working traffic enforcement in a primarily urban environment. The blood samples of these officers had an average lead concentration of 124.32 µg/l and a SD of 37.74 µg/l; a previous study of individuals from a nearby suburb, with no history of exposure, found an average blood level concentration of 35 µg/l. Test the hypothesis that the downtown police officers have a higher lead exposure than the group in the previous study. Interpret your results in context. Based on your preceding result, without performing a calculation, would a 99% confidence interval for the average blood concentration level of police officers contain 35 µg/l? Based on your preceding result, without performing a calculation, would a 99% confidence interval for this difference contain 0? Explain why or why not.A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.141.14. A dietician is asked to test this claim and finds that a random sample of 2424 servings has a variance of 0.950.95. At alpha equals 0.10α=0.10, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed.
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- The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with σ = .3. Assume that the sample mean is 5.25. (a) Does this indicate that the true average percentage differs from 5.5? Carry out a test at α = .01. (b) If the true average percentage is µ = 5.6, what is the probability of type II error?The average UQ student reports dedicating 8.5 hours per week to each 2-unit course. What is the approximate t obtained value for a group of 20 psychology students who study for a mean of 10 hours per week for each 2-unit course, where the estimated population variance is 9. Would this sample be considered significantly different from the population, applying an alpha level of 0.05? t = 0.67; the sample would be considered statistically significant t = 2.24; the sample would be considered statistically significant t = 2.24; the sample would NOT be considered statistically significant t = 0.67; the sample would NOT be considered statistically significant