1.The American Water Works Association reports that the per capita water use in a single-family home is 65 gallons per day. Legacy Ranch is a relatively new housing development. The builders installed more efficient water fixtures, such as low-flush toilets, and subsequently conducted a survey of the residences. Twenty-one owners responded, and the sample mean water use per day was 63 gallons with a standard deviation of 9.1 gallons per day.

At the 0.10 level of significance, is that enough evidence to conclude that residents of Legacy Ranch use less water on average?

a. What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

Reject H0: 65 and fail to reject H1: < 65 when the test statistic is (less or greater than) _______ _______

b. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

?Value of the test statistic_______

2.A cola-dispensing machine is set to dispense 11 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manufacturer of the machine would like to set the control limit in such a way that, for samples of 42, 5% of the sample means will be greater than the upper control limit, and 5% of the sample means will be less than the lower control limit.

a. At what value should the control limit be set? (Round z values to two decimal places. Round your answers to 2 decimal places.)

?Value should be in between______and_____

b. If the population mean shifts to 10.5, what is the probability that the change will not be detected? (Round your intermediate calculations to 2 decimal places and finalanswer to 4 decimal places.)

?Probability_______

c. If the population mean shifts to 11.4, what is the probability that the change will not be detected? (Round your intermediate calculations to 2 decimal places and finalanswer to 4 decimal places.)

?Probability_______

3.A national grocer's magazine reports the typical shopper spends 5 minutes in line waiting to check out. A sample of 15 shoppers at the local Farmer Jack's showed a mean of 4.2 minutes with a standard deviation of 3.8 minutes.

Is the waiting time at the local Farmer Jack's less than that reported in the national magazine? Use the 0.010 significance level.

a. What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

Reject H0: 5 and fail to reject H1: < 5 when the test statistic is______ _______.

b. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

?Value of the test statistic______

4.A sample of 50 observations is selected from a normal population. The sample mean is 65, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level.

H₀: = 66

H₁: 66

?There is a________% chance of finding a z value this large by "sampling error" when H0 is true.