Question

An Izod Impact Test was performed on 20 specimens of PVC pipe. The sample mean is ? = 1.25, and the sample ??? ??????? ? standard deviation is ? = 0.25. You need to test if the true mean Izod Impact Strength is less than 1.5.

a.Write down the Null and Alternative Hypotheses to be tested

b.What is the appropriate type of statistical test? Explain.

c.Construct a 95% ?????????? ???????? and test the Hypotheses. Clearly interpret the test result.

d.Test the Hypotheses using the Test Statistic method. Do you get the same answer as part (c)?

c. What is the ? ????? for the test? Do you get the same answer as parts (c) and (d)?

Answer 1

a) As we are testing here whether the true mean Izod Impact Strength is less than 1.5, therefore the null and the alternative hypothesis here are given as:

b) As the sample size here is 20 is small and the true population standard deviation is unknown, we would be conducting a t test here.

c) For n - 1 = 19 degrees of freedom, we get from the t distribution tables as:
P( t19 < 2.093) = 0.975

Therefore, due to symmetry, we get here:
P( - 2.093 < t19 < 2.093) = 0.95

Therefore the confidence interval here is obtained as:

This is the required 95% confidence interval for the population mean. As the value of 1.5 lies outside the given interval, therefore we can reject the null hypothesis here and conclude that we have sufficient evidence that the true mean is not equal to 1.5

d) The test statistic here is computed as:

For n - 1 = 19 degrees of freedom, we get from the t distribution tables:

P( t19 < -4.4721) = 0.0001

As the p-value here is 0.0001 < 0.05 which is the level of significance here, therefore we can reject the null hypothesis here and therefore we get the same result here as the previous part.

the p-value for the test is 0.0001