1. The following table provides lap times for Lap 4 from a racer's log book. Times are recorded in seconds for 2.5-mile laps completed in a series of races and practice runs. Use the data to test the claim that the racer finishes Lap 4, on average, in less than 129 seconds. Use all twenty races given. Conduct a hypothesis test at the 5% level.

Race Lap Times (in Seconds)
	Lap 4
Race 1	128
Race 2	132
Race 3	128
Race 4	131
Race 5	126
Race 6	132
Race 7	128
Race 8	131
Race 9	131
Race 10	129
Race 11	127
Race 12	125
Race 13	128
Race 14	131
Race 15	128
Race 16	130
Race 17	131
Race 18	129
Race 19	130
Race 20	130

Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

(i)What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)

(ii)Construct a 95% confidence interval for the true mean. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to two decimal places.)

2. The following table provides lap times for Lap 4 from a racer's log book. Times are recorded in seconds for 2.5-mile laps completed in a series of races and practice runs. Use the data to test the claim that the racer finishes Lap 4, on average, in less than 129 seconds. Use all twenty races given. Conduct a hypothesis test at the 5% level.

Race Lap Times (in Seconds)
	Lap 4
Race 1	132
Race 2	133
Race 3	129
Race 4	129
Race 5	130
Race 6	128
Race 7	130
Race 8	129
Race 9	128
Race 10	131
Race 11	128
Race 12	131
Race 13	127
Race 14	130
Race 15	132
Race 16	131
Race 17	125
Race 18	131
Race 19	131
Race 20	130

Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

(i)What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)

(ii) What is the p-value? (Round your answer to four decimal places.)

(iii)Construct a 95% confidence interval for the true mean. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to two decimal places.)