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
Step-by-step 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