Question

Question 2

A manufacturer of sprinkler systems used for fire protection in office buildings claims that the true average system-activation temperature is 130 degrees. A sample of 9 systems when tested yields a sample average activation temperature of 131.08 degrees. If the distribution of activation times is normal with standard deviation 1.5 degrees, test at the 1% level of significance to see if the data shows evidence that is different from the manufacturers claim. (a) State the null and alternative hypotheses for the test. [2 marks] (b) What is the test statistic? [1 mark](c) Calculate the value of the test statistic for this test. [2 marks] (d) Calculate the p-value for this test. [2 marks] (e) State the conclusion of this test. Give a reason for your answer. [3 marks] Total 10 marks

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 130
Alternative Hypothesis, Ha: μ ≠ 130

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (131.08 - 130)/(1.5/sqrt(9))
z = 2.16

P-value Approach
P-value = 0.0308

As P-value >= 0.01, fail to reject null hypothesis.

not different than population mean