Question

D" size batteries produced by MNM Corporation have had a life expectancy of 87 hours. Because of an improved production process, the company believes that there has been an INCREASE in the life expectancy of its D size batteries. A sample of 36 improved batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours. Use a .01 level of significance, and test to determine if there has been an increase in the life expectancy of the D size batteries.

Group of answer choices

z = 1; therefore do not reject H0. There is not sufficient evidence at α = .01 to conclude that there has been an increase in the life expectancy in the D size batteries.

z = 1; therefore reject H00000. There is not sufficient evidence at ααααα = .01 to conclude that there has been an increase in the life expectancy in the D size batteries.

z = 1; therefore do not reject H00000. There is sufficient evidence at ααααα = .01 to conclude that there has been an increase in the life expectancy in the D size batteries.

z = 2; therefore do not reject H000. There is sufficient evidence at ααα = .01 to conclude that there has been an increase in the life expectancy in the D size batteries.

Answer 1

Answer:

z = 1; therefore do not reject H0. There is not sufficient evidence at α = .01 to conclude that there has been an increase in the life expectancy in the D size batteries.

Explanation:

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

H₀: µ = 87 versus H_a: µ > 87

This is an upper tailed test.

The test statistic formula is given as below:

Z = (x̄ - µ)/[σ/sqrt(n)]

From given data, we have

µ = 87

x̄ = 88.5

σ = 9

n = 36

α = 0.01

Critical value = ± 2.3263

(by using z-table or excel)

Z = (88.5 - 87)/[ 9/sqrt(36)]

Z = 1.0000

P-value = 0.1587

(by using Z-table)

P-value > α = 0.01

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that there has been an increase in the life expectancy in the D size batteries.