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Use the following information to answer the next $15$exercises: Indicate if the hypothesis test is for

a. independent group means, population standard deviations, and/or variances known

b. independent group means, population standard deviations, and/or variances unknown

c. matched or paired samples

d. single mean

e. two proportions

f. single proportion

It is believed that the average grade on an English essay in a particular school system for females is higher than for males. A random sample of $31$females had a mean score of $82$ with a standard deviation of three, and a random sample of $25$ males had a mean score of $76$ with a standard deviation of four

What are the sample mean difference?

Use the following information to answer next five exercises. A study was conducted to test the effectiveness of a juggling class. Before the class started, six subjects juggled as many balls as they could at once. After the class, the same six subjects juggled as many balls as they could. The differences in the number of balls are calculated. The differences have a normal distribution. Test at the $1\%$ significance level

What is the sample mean difference?

Use the following information to answer next five exercises. A study was conducted to test the effectiveness of a juggling class. Before the class started, six subjects juggled as many balls as they could at once. After the class, the same six subjects juggled as many balls as they could. The differences in the number of balls are calculated. The differences have a normal distribution. Test at the $1\%$ significance level.

What conclusion can you draw about the juggling class?

Use the following information to answer the next five exercises. A doctor wants to know if a blood pressure medication is effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the $1\%$significance level.

What is the sample mean difference?

The mean number of English courses taken in a two–year time period by male and female college students is believed
to be about the same. An experiment is conducted and data are collected from 29 males and 16 females. The males took an
average of three English courses with a standard deviation of 0.8. The females took an average of four English courses with
a standard deviation of 1.0. Are the means statistically the same?

A student at a four-year college claims that mean enrollment at four–year colleges is higher than at two–year colleges in the United States. Two surveys are conducted. Of the \(35\) two–year colleges surveyed, the mean enrollment was \(5,068\) with a standard deviation of \(4,777\). Of the \(35\) four-year colleges surveyed, the mean enrollment was \(5,466\) with a standard deviation of \(8,191\).

The league mean batting average is 0.280 with a known standard deviation of 0.06. The Rattlers and the Vikings belong

to the league. The mean batting average for a sample of eight Rattlers is 0.210, and the mean batting average for a sample

of eight Vikings is 0.260. There are 24 players on the Rattlers and 19 players on the Vikings. Are the batting averages of the

Rattlers and Vikings statistically different?

At Rachel’s \(11th\) birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis.

Mean entry-level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. A recruiting office thinks that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. The recruiting office randomly surveys \(50\) entry level mechanical engineers and \(60\) entry level electrical engineers. Their mean salaries were \(\$46,100\) and \(\$46,700\), respectively. Their standard deviations were \(\$3,450\) and \(\$4,210\), respectively. Conduct a hypothesis test to determine if you agree that the mean

entry-level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.