Question

The abc battery company claims that their batteries last 100 hours, on average. you decide to conduct a test to see if the company's claim is true. you believe that the mean life may be different from the 100 hours the company claims. you decide to collect data on the average battery life (in hours) of a random sample of n = 20 batteries. some of the information related to the hypothesis test is presented below.

Answer 1

Complete question is;

The abc battery company claims that their batteries last 100 hours, on average. You decide to conduct a test to see if the company's claim is true. You believe that the mean life may be different from the 100 hours the company claims. you decide to collect data on the average battery life (in hours) of a random sample of n = 20 batteries. some of the information related to the hypothesis test is presented below:

Test of H0: μ = 100 versus H1: μ ≠ 100

Sample mean: 98.5

Std error of mean: 0.777

Assuming the life length of batteries is normally distributed, what is the p-value associated with this test?

Answer:

p-value =  0.00001

Explanation:

We are given;

Null hypothesis; H0: μ = 100

Alternative Hypothesis; H1: μ ≠ 100

Sample mean: x = 98.5

Standard error of mean; s = 0.777

To find the test statistic, we will use the formula;

t = (x - μ)/(s/√n)

t = (98.5 - 100)/(0.777/√20)

t = -1.5/0.1737

t = -8.64

Now, from online p-value from t-score calculator attached, using t = -8.64; DF = n - 1 = 20 - 1 = 19; two tail distribution;significance level of 0.05; we have;

The p-value =  0.00001