(See attached file for full problem description with all symbols)

1. A coin-operated drink machine was designed to discharge a meanof ounces of coffee per cup. Suppose that we want to carry out a hypothesis testto see if the true mean discharge differs from . State the null hypothesis and the alternative hypothesis that we would use for this test.

Ho: ________________________

H1: ________________________

2. 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.

Ho: ________________________

H1: ________________________

3. A furniture store claims that a specially ordered product will take, on average, = days (4 weeks) to arrive. The standard deviationof these waiting times is days. We suspect that the special orders are taking longer than this. To test this suspicion, we track a random sampleof special orders and find that the orders took a mean of days to arrive. Can we conclude at the level of significance that the mean waiting time on special orders at this furniture store exceeds 28 days?

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.

The Null Hypothesis Ho: ________________

The Alternative Hypothesis: H1: ________________

The type of test statistic: _________________

The value of the test statistic: _________________

The p-value: __________________

Can we conclude that the mean waiting time on special orders at the furniture store exceeds 29 days. YES or NO

4. A manufacturer claims that the mean lifetime, , of its light bulbs is months. The standard deviation of these lifetimes is months. Ninety 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.

The Null Hypothesis Ho: ___________________

The Alternative Hypothesis: H1: ___________________

The type of test statistic: _____________________

The value of the test statistic: _____________________

The two critical values at the 0.01 level of significance: ____________________

Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 44 months? _______________________

5. A college professor claims that the entering class this year appears to be smarter than entering classes from previous years. He tests a random sample of of this year’s entering students and finds that their mean IQ score is , with standard deviation of . The college records indicate that the mean IQ score for entering students from previous years is . If we assume that the IQ scores of this year’s entering class are normally distributed, is there enough evidence to conclude, at the level of significance, that the mean IQ score, , of this year’s class is greater than that of previous years?

Perform a one-tailed test.

The Null Hypothesis Ho: ______________________

The Alternative Hypothesis: H1: ______________________

The type of test statistic: ________________________

The value of the test statistic: ________________________

The two critical values at the 0.05 level of significance: _____________________

Can we conclude, using the 0.05 level of significance, that the mean IQ score of this year’s class is greater than that of previous years? YES or NO

6. 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

The Null Hypothesis Ho: ____________________

The Alternative Hypothesis: H1: ____________________

The type of test statistic: ______________________

The value of the test statistic: ______________________

The two critical values at the 0.01 level of significance: ______________________

Using the 0.1 level of significance, can we conclude that the mean monthly rent for apartments on the east side is less than $750? YES or NO

To state null and alternative hypothesis of given problems.