Question

I.   Before accepting a large shipment of bolts, the director of an elevator construction project checks
The tensile strength of a simple random sample consisting of 20 bolts. She is concerned that the bolts may be counterfeits, which bear the proper markings for this grade of bolt, but are made from inferior materials. For this application, the genuine bolts are known to have a tensile strength that is normally distributed with a mean of 1400 pounds and a standard deviation of 30 pounds. The mean tensile strength for the bolts tested is 1385 pounds.

a. Formulate and carry out a hypothesis test, using the critical value approach and at a 3% level of significance to examine the possibility that the bolts in the shipment might not be genuine. Be sure to show all the steps of this approach i.e..1. state H0 and HA, 2. select α, select the test statistic (giving reason for your choice), and compute it, 3. get the critical value, 4 .compare the test statistic, 5. state your decision, and 6. explain (interpret) your conclusion   

b.   Identify and interpret the p-value for the test.

Answer 1

a)

The test hypothesis is

This is a two-sided test because the alternative hypothesis is formulated to detect differences from the hypothesized mean value of 30 on either side.

Now, the value of test static can be found out by following formula:

Since t0 = 2.2361 < -2.345647533562372 = -t{0.015}, we fail to reject the null hypothesis

We have insufficient evidence to claim that the bolts in the shipment might not be genuine

b)

Using Excel's function =T.DIST.2T(|t0|,n-1), the P-value for t0 = 2.2361 in an t-test with 19 degrees of freedom can be computed as