A producer of various kinds of batteries has been producing "D" size batteries with a life expectancy of 87 hours. Due to an improved production process, management believes that there has been an increase in the life expectancy of their "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. It is known that the standard deviation of the population is 9 hours
a. Give the null and the alternative hypotheses.
b. Compute the test statistic.
c. At the 1% level of significance using the critical value approach, test management's belief.
d. What is the p-value associated with the sample results? What is your conclusion based on the p-value using ? = .01?
e. What is your conclusion based on the p-value using ? = .05?
a. H0: ? < 87 hours
Ha: ? > 87 hours
b. 1.00
c. Since z = 1 < 2.33, do not reject H0
d. p-value = .1587 > .01; therefore do not reject H0 and conclude that there is insufficient evidence to support the management's belief.
e. p-value = .1587 > .05; therefore, do not reject H0; no evidence to support the management's belief using the 5% level of significance.
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