The lifetimes (in hours) of a sample of 30 AA batteries produced by some company are measured. The data are shown below:
58 117 99 74 63 100 88 37 60 124 92 28 77 56 68 112 84 40 129 94
112 75 82 101 95 67 52 118 93 110
It is known that the standard deviation of all AA batteries produced by this company is 25 hours. The sample mean is calculated to be x = 83:5.
(a) We would like to use inference procedures to estimate and test for the true mean lifetime of all AA batteries produced by this company. However, we dont know whether lifetimes follow a normal distribution. Explain why it is nevertheless appropriate to use inference procedures which rely on the assumption of normality.
(b) Calculate a 97% confidence interval for the true mean lifetime of all AA batteries produced by this company.
(c) Provide an interpretation of the interval you constructed in (b).
(d) Conduct an appropriate hypothesis test at the 3% level of significance to determine whether the true mean lifetime of all AA batteries produced by this company differs from 75 hours. Use the P-value approach.
(e) Provide an interpretation of the P-value of the test in (d).
(f) Use JMP to verify your results in (d). Include the JMP output in your assignment and highlight the value of the test statistic and the P-value.
(g) Could the interval in (b) have been used to conduct the test in (d)? If no, explain why not. If yes, explain why, and explain what your conclusion would have been and why.