The piston diameter of a certain hand pump is 0.56 inch. The manager determines that the diameters are normallydistributed, with a mean of 0.56 inch and a standard deviation of 0.005 inch. After recalibrating the productionmachine, the manager randomly selects 26 pistons and determines that the standard deviation is 0.0035 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the =0.10 level ofsignificance?

1. Are the requirements met to perform thistest? Because the sample is/is not obtained using simple random sampling and the population is/is not normallydistributed, the requirements for testing the hypothesis are/are not satisfied.
2. What are the correct hypotheses for thistest? H0: versus H1: (Type integers or decimals. Do notround.)
3. Calculate the value of the test statistic
4. Approximate theP-value for the test statistic. Choose the correct answer below.

• A.TheP-value is between0.05and0.10.
• B.TheP-value is greaterthan0.10.
• C.TheP-value is between0.025and0.05.
• D.TheP-value is between0.01and0.025.
• E.TheP-value is lessthan0.005.
• F.TheP-value is between0.005and0.01.

What is the correct conclusion at the =0.10 level ofsignificance?

Since theP-value is the level ofsignificance, the null hypothesis. There evidence to conclude that the standard deviation has decreased at the 0.10 level of significance.