1.On the basis of her newly developed technique, a student believes she can reduce the amount of time schizophrenics spend in an institution. As director of training at a nearby institution, you agree to let her try her method on 17 schizophrenics, randomly sampled from your institution. The mean duration that schizophrenics stay at your institution is 85 weeks, with a standard deviation of 12 weeks. The scores are normally distributed. The results of the experiment show that the patients treated by the student stay a mean duration of 80 weeks, with a standard deviation of 20 weeks

(c) What do you conclude about the student’s technique? Use α = 0.052 tail.

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2.A gasoline manufacturer believes a new additive will result in more miles per gallon. A large number of mileage measurements on the gasoline without the additive showed a mean of 24.7 miles per gallon and a standard deviation of 4.8. An experiment was performed in which 75 cars were tested using the gasoline plus the additive. The results showed a sample mean of 26.5 miles per gallon. To evaluate these data, a directional test withα= 0.051 tailwas used. Suppose that before doing the experiment, the manufacturer wants to determine the probability that he will be able to detect a real mean increase of 2.0 miles per gallon with the additive if the additive is at least that effective.

(a) If he tests 20 cars, what is the power to detect a mean increase of 2.0 miles per gallon?(c) How many cars should he use if he wants to have a 99% chance of detecting a mean increase of 2.0 miles per gallon?

3.

A physical education professor believes that exercise can slow the aging process. For the past 10 years, he has been conducting an exercise class for 14 individuals who are currently 50 years old. Normally, as one ages, maximum oxygen consumption decreases. The national norm for maximum oxygen consumption in 50-year-old individuals is 30 milliliters per kilogram per minute, with a standard deviation of 9.5. The mean of the 14 individuals is 36 milliliters per kilogram per minute. What do you conclude? Use α = 0.051 tail.

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4.The chairperson of a psychology department believes the Ph.D. program of her department is particularly good; that it attracts exceptional graduate students, and consequently, the Ph.D. students of her department earn their Ph.D.’s in significantly less time than do their counter parts in other psychology departments. To test this belief, she compares the time it took students to earn their Ph.D.’s in her department over the past three years, with national data for the same time period. In the past three years, this department has awarded 35 Ph.D.’s; the mean time to obtain the Ph.D. was 62.0 months, with a standard deviation of 6.2 months. National data for psychology departments throughout the United States compiled for that time showed that the mean time to obtain a Ph.D. was 78.4 months, with a standard deviation of 11.7 months, and the distribution of these scores was normally distributed.

(c) Using α = 0.012 tail, what do you conclude?

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Question-1:Null hypothesis, H0 : 0 Alternative hypothesis, Student believes her new technique will reduce the amount ofH1 :time schizophrenics spend in an institution.Level of significance,…