4. Procedure for hypothesis testing the mean:

1. Identify H0 and Ha from the claim.

2. Determine if the hypothesis test is a left test or a right test.

3. Use the t-distribution with , /2, and df = n - 1

4. Find the test statistic

5. Find the P-value of the test statistic and compare it to the significance

6. Determine if we should reject or fail to reject the null hypothesis.

7. report final conclusion

The amounts of water consumed per week by Montan residents are normally distributed with an unknown mean and a standard deviation of 10 gallons. A simple random sample of 16 residences has a mean value of x = 120.3 gallons. The city of Bozeman claims that the average water consumed in the state of Montana is not 125 gallons. Test the claim at the 0.05 significance level.

5. A used car dealer says that the mean price of a 2016 Honda CR-V is at least $27,000. You suspect this claim is incorrect and find that a random sample of 11 similar vehicles has a mean price of $21,850 and a standard deviation of $1,084. Is there enough evidence to reject the dealer's claim at = 0.05?

6. The level of dissolved oxygen (DO) in a stream or river is an important indicator of the water's ability to support aquatic life. A researcher measures the DO level at 15 randomly chosen locations along a stream. Here are the results in milligrams per liter (mg/l) 4.53 5.04 3.29 5.23 4.13 5.5 4.83 4.40 5.42 6.38 4.01 4.66 2.87 5.73 5.55 A dissolved oxygen level below 5mg/l puts aquatic life at risk.

(a) Can you conclude that aquatic life in the stream is at risk at a significance level of = 0.05?

(b) Given your conclusion in part (a), which kind of mistake (a Type I or Type II error) could have been made? Explain what this mistake would mean in context.