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# Testing of Hypothesis

Last year's mean hourly wage (in dollars) for all hospital clerical workers in a large state was
See attached file for full problem description.

An administrator for the state believes that this year's mean hourly wage for hospital clerical workers is greater than last year's mean. She hires statisticians to sample a number of hospital clerical workers and to carry out a hypothesis test. State the null hypothesis and the alternative hypothesis that would be used for this test.
What is the ?
What is the ?

It is claimed that the proportion of high school students in the United States who use computers for educational purposes is at most . Suppose that we have reason to believe otherwise and wish to carry out a hypothesis test for this claim. State the null hypothesis and the alternative hypothesis that we would use for this test.
What is the ?
What is the ?

An automobile assembly line operation has a scheduled mean completion time, , of minutes. The standard deviation of completion times is minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of completion times under new management was taken. The sample had a mean of minutes. Can we support, at the level of significance, the claim that the mean completion time has decreased under new management? Assume that the standard deviation of completion times has not changed.
Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table.
What's the null hypothesis?
What's the alternative hypothesis?
The type of test statistic Z t Chi Square F
What's the value of the test statistic? Round to at least three decimal places.
Can we support the claim that the mean completion time has decreased under new management? YES or NO

The breaking strengths of cables produced by a certain manufacturer have a mean, , of pounds, and a standard deviation of pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be pounds. Assume that the population is normally distributed. Can we support, at the level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.)
Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table.
What's the null hypothesis?
What's the alternative hypothesis?
The type of test statistic Z t Chi Square F
What's the value of the test statistic? Round to at least three decimal places.
Can we support the claim that the mean breaking strength has increased? YES or NO

Loretta, who turns this year, has heard that the mean systolic blood pressure among the elderly is millimeters of mercury (mmHg), but she believes that the actual value is higher. She bases her belief on a recently reported study of randomly selected, elderly adults. The sample mean systolic blood pressure of the adults in the study was mmHg, and the sample standard deviation was mmHg.
Assume that the population of systolic blood pressures of elderly adults is normally distributed. Based on the study, at the level of significance, can it be concluded that , the mean systolic blood pressure among elderly adults, is greater than mmHg?
Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table
What's the null hypothesis?
What's the alternative hypothesis?
The type of test statistic Z t Chi Square F
What's the value of the test statistic? Round to at least three decimal places.
Can it be concluded, at the 0.05 level of significance, that mean systolic blood pressure among elderly adults is greater than 115mmHg? YES or NO

A rental agent claims that the mean monthly rent, , for apartments on the east side of town is less than . A random sample of monthly rents for apartments on the east side has a mean of , with a standard deviation of . If we assume that the monthly rents for apartments on the east side are normally distributed, is there enough evidence to conclude, at the level of significance, that is less than ?
Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.
What's the null hypothesis?
What's the alternative hypothesis?
The type of test statistic Z t Chi Square F
Using the 0.05 level of significance, can we conclude that the mean monthly rent for apartments on the east side is less than \$675? YES or NO

The mean height of a certain kind of plant is centimeters. Suppose we want to carry out a hypothesis test to see if the mean height of plants treated with a certain chemical differs from . State the null hypothesis and the alternative hypothesis that we would use for this test.
What is the ?
What is the ?

The mean height of a certain kind of plant is centimeters. Suppose we want to carry out a hypothesis test to see if the mean height of plants treated with a certain chemical differs from . State the null hypothesis and the alternative hypothesis that we would use for this test.
What is the ?
What is the ?

A manufacturer claims that the mean lifetime, , of its light bulbs is months. The standard deviation of these lifetimes is months. Eighty bulbs are selected at random, and their mean lifetime is found to be months. Can we conclude, at the level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from months?
Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table.
What's the null hypothesis?
What's the alternative hypothesis?
The type of test statistic Z t Chi Square F
What's the value of the test statistic? Round to at least three decimal places.
The p-value? Round to at least three decimal places.
Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 54 months? YES or NO

The breaking strengths of cables produced by a certain manufacturer have a mean, , of pounds, and a standard deviation of pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be pounds. Assume that the population is normally distributed. Can we support, at the level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.)
Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table.
What's the null hypothesis?
What's the alternative hypothesis?
The type of test statistic Z t Chi Square F
What's the value of the test statistic? Round to at least three decimal places.
The critical value at the 0.05 level of significance? Round to at least three decimal places.
Can we support the claim that the mean breaking strength has increased? YES or NO

#### Solution Summary

To test if mean is significantly different.

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