The McCollough Corporation, a producer of various kinds ofbatteries, has been producing \"D\" size batteries with a lifeexpectancy of 87 hours. Due to an improved production process, themanagement believes that there has been an increase in the lifeexpectancy of their \"D\" size batteries. A sample of 36 batteriesshowed an average life of 88.5 hours. Assume from past informationthat it is known that the standard deviation of the population is 9hours.
a. Use a 0.01 level of significance to test for the evidence ofimprovement in the life expectancy of the batteries. Use thecritical value criterion in your decision making.
[Hint: You need to (1) write the null and alternative hypotheses(2) know the significance level of the test (3) write theappropriate formula for the teststatistic (4) using the sampledata, compute the numerical value of the teststatistic (5) look upthe critical value, and finally (6) draw your conclusion].
b. What is the p-value of the test? Draw your conclusion usingthe p-value criterion.
