Question

A supplier submits lote of fabric to a textile manufacturer. The customer wants to know if the lot average breaking strength exceeds 200 psi. If so, he wants to accpt the lot. Past experience indicates that a reasonable value for the variance of breaking strength is 100 (psi)2.. Four specimens are randomly selected and the average breaking strength observed is 214 psi. Perform a hypothesis test (7 step procedure outlined in class). Perform the test using the Fixed significance level test and the P-Value approach test and state your decision.

Answer 1

Step 1:

H0: Null Hypothesis: 200 ( the lot average breaking strength does not exceed 200 psi.)

Step 2:

HA: Alternative Hypothesis: 200 ( the lot average breaking strength exceeds 200 psi.) (Claim)

Step 3:

Take Significance Level = = 0.05

From Table, critical value of Z = 1.64

Step 4:

n = 4

= 214

=

Step 5:
Test Statistic is given by:

Step 6:

Rejection Region:
Reject H0 if Z > 1.64

Step 7:

Since calculated value of Z = 2.80 is greater than critical value of Z= 1.64, the difference is significant. Reject null hypothesis.

Step 8:

Conclusion::
The data support the claim that the lot average breaking strength exceeds 200 psi.

P Value approach:

By Technology, p - value = 0.0026.

Since p - value =0.0026 is less than = 0.05, the difference is significant. Reject null hypothesis.

Conclusion::
The data support the claim that the lot average breaking strength exceeds 200 psi.