As the principal of a private high school, you are interested in finding out how the training in mathematics at your school compares with that of the public schools in your area. For the last 5 years, the public schools have given all graduating seniors a mathematics proficiency test. The distribution has a mean of 75. You give all the graduating seniors in your school the same mathematics proficiency test. The results show a distribution of 26 scores, with a mean of 82 and a standard deviation of 13.

Using α = 0.052 tail, what do you conclude?
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A student conducted an experiment on 25 schizophrenic patients to test the effect of a new technique on the amount of time schizophrenics need to stay institutionalized. The results showed that under the new treatment, the 25 schizophrenic patients stayed a mean duration of 78 weeks, with a standard deviation of 20 weeks. Previously collected data on a large number of schizophrenic patients showed a normal distribution of scores, with a mean of 85 weeks and a standard deviation of 15 weeks. These data were evaluated using α = 0.052 tail. The results showed a significant effect. Assume that the standard deviation of the population is unknown. Using α = 0.052 tail, what do you conclude about the new technique?

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A sample set of 29 scores has a mean of 76 and a standard deviation of 7. Can we accept the hypothesis that the sample is a random sample from a population with a mean greater than 72? Use α = 0.011 tail in making your decision

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A local business school claims that their graduating seniors get higher-paying jobs than the national average for business school graduates. Last year's figures for salaries paid to all business school graduates on their first job showed a mean of $10.20 per hour. A random sample of 10 graduates from last year's class of the local business school showed the following hourly salaries for their first job: $9.40, $10.30, $11.20, $10.80, $10.40, $9.70, $9.80, $10.60, $10.70, $10.90. You are skeptical of the business school claim and decide to evaluate the salary of the business school graduates using α = 0.052 tail.

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Is it reasonable to consider a sample with N = 22, Xobt = 42, and s = 9 to be a random sample from a normal population with μ = 38? Use α = 0.051 tail in making your decision. Assume Xobt is in the right direction.
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A developmental psychologist is interested in whether tense parents tend to have tense children. A study is done involving one parent for each of 12 families and the oldest child in each family, measuring tension in each pair. Pearsonr = 0.596. Using α = 0.052 tail, is the relationship significant?

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A cognitive psychologist believes that a particular drug improves short-term memory. The drug is safe, with no side effects. An experiment is conducted in which 8 randomly selected subjects are given the drug and then given a short time to memorize a list of 10 words. The subjects are then tested for retention 15 minutes after the memorization period. The number of words correctly recalled by each subject is as follows: 7, 8, 12, 5, 10, 6, 8, 7. Over the past few years, the psychologist has collected a lot of data using this task with similar subjects. Although he has lost the original data, he remembers that the mean was 5 words correctly recalled and that the data were normally distributed.
On the basis of these data, what can we conclude about the effect of the drug on short-term memory? Use α= 0.052 tail in making your decision.

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A physician employed by a large corporation believes that due to an increase in sedentary life in the past decade, middle-age men have become fatter. In 1995, the corporation measured the percentage of fat in their employees. For the middle-age men, the scores were normally distributed, with a mean of 22%. To test her hypothesis, the physician measures the fat percentage in a random sample of 12 middle-age men currently employed by the corporation. The fat percentages found were as follows: 24, 40, 29, 32, 33, 25, 15, 22, 18, 25, 16, 27. On the basis of these data, can we conclude that middle-age men employed by the corporation have become fatter? Assume a directional H1 is legitimate and use α = 0.051 tail in making your decision.

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A sample set of 30 scores has a mean of 15.0 and a standard deviation of 6.0. Is it reasonable to assume that the sample is a random sample from a population set of scores with a mean of 18.0? In drawing your conclusion, assume the population is normally distributed and use α = 0.052 tail.

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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 an unknown standard deviation, and the distribution of these scores was normally distributed.

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A sample set of 20 scores has a mean equal to 81 and a standard deviation of 11. Can we reject the hypothesis that this sample is a random sample from a normal population with μ = 77? Use α = 0.012 tail in making your decision.

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A college counselor wants to determine the average amount of time first-year students spend studying. He randomly samples 25 students from the freshman class and asks them how many hours a week they study. The mean of the resulting scores is 23 hours, and the standard deviation is 6.4 hours.
(a) Construct the 95% confidence interval for the population mean.

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(b) Construct the 99% confidence interval for the population mean.

-A professor in the women's studies program believes that the amount of smoking by women has increased in recent years. A complete census taken 2 years ago of women living in a neighboring city showed that the mean number of cigarettes smoked daily by the women was 5.4 with a standard deviation of 2.5. To assess her belief, the professor determined the daily smoking rate of a random sample of 200 women currently living in that city. The data show that the number of cigarettes smoked daily by the 200 women has a mean of 6.1 and a standard deviation of 2.7.
Is the professor's belief correct? Assume a directional H1 is appropriate and use α = 0.051 tail in making your decision. Be sure that the most sensitive test is used to analyze the data.

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(b) Assume the population mean is unknown and reanalyze the data using the same alpha level. What is your conclusion this time?
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