Q1. Use the distribution tables to determine the following values.

1. Let =0.04=0.04 find values z,z/2z,z/2.

2. Let =0.2=0.2 find values t(5),t/2(5),t(13),t/2(13)t(5),t/2(5),t(13),t/2(13).

Q2. The insurance company would like to compare the repair cost of moderately damaged cars in two different garages: A and B. They take a sample of n=7 cars which are moderately damaged. These cars are sent to two garages to obtain repair cost estimate. Assume the cost difference is normally distributed. The insurance company wants to test ifthegarage A provides more expensive service than the garage B, Let a=0.01

Car / Cost of A / Cost of B

1 / 7.9 / 7.1

2 / 10.1 / 9.0

3 / 12.2 / 11.0

4 / 8.8 / 8.9

5 / 10.4 / 9.9

6 / 9.8 / 9.1

7 / 11.7 / 10.3

Q3. Many scientists are concerned about changes in the ice thickness due to global warming. Suppose the historical mean thickness of the ice just off the coast of Barrow, Alaska, is 3.32 meters. A recent random sample (n=28n=28) of the ice thickness near Barrow was obtained. The sample mean ice thickness is 4.036 meters. Assume =2.8=2.8 meters, and the underline distribution is normal. Conduct a hypothesis test to determine whether there is any change in the mean ice thickness. Use =0.01=0.01.

Q4. Manatees are one creature found in coastal waterways. 10 years ago, researchers concluded that the true mean weight of manatees was approximately 1050 lbs. This year, a random sample of 12 manatees were selected, the sample weights are: 956, 1012, 954, 988, 973, 1048, 1075, 1064, 856, 1026, 1031, 1064. Assume the underlying distribution of manatee weights is normal, and population standard deviation is unknown.

1. Implement a hypothesis test to verify if there is any evidence to suggest the true mean weight decreases now. Solve the hypothesis using PP-value method. Let =0.05.=0.05.

2. Use the given sample data to calculate 90% confidence interval for true mean weight of manatees.

Q5. Manatees are one creature found in coastal waterways. To study this creature, a random sample of 12 manatees were selected, the sample manatees were released before their weights (in pounds) were carefully recorded: 956, 1012, 954, 988, 973, 1048, 1075, 1064, 856, 1026, 1031, 1064. Assuming the underlying distribution of manatee weights is normal, with population standard deviation of =63=63 pounds.

1. Find a 95% confidence interval for the true mean weight.

2. Find the large enough sample size such that the margin of error of a 98% confidence interval is 20 pounds.

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