NAME:
Breaking Strength (lbs) | ||
Fiber | Mean | Variance |
New | 59.3 | 12.1 |
Present | 55.6 | 11.9 |
Conduct an hypothesis test, at the 0.01 level of significance, to compare the strengths of the two fibers. To do so, please answer the following.
The two sample C+E model for independent populations.
versus , where is the mean breaking strength of the new fiber, and is the mean breaking strength of the present fiber.
. The pooled variance test is chosen because the sample variances are very close.
First, we compute . Now
sp2=((12-1)(12.1)+(12-1)(11.9))/22=12, so that
.
The observed value of the test statistic is then .
Using the t tables to compare this with the t22 distributiion, we get the p-value:
. From the table, we find that the p-value lies between 0.005 and 0.01.
(1) Normality (2) Equal population variances
Reject H0 in favor of Ha at the 0.01 level of significance. Conclude that the mean strength of the new fiber is greater than that of the present fiber.
The p-value is , where . From the normal table, we see that z*u must lie between 1.82 and 1.95. Therefore, y* must lie between , and . Since y* must be an integer, y*=72.