Question

The breaking strength of a thread used in the manufacture of upholstery material is required to be at least 100psi (pounds per square inch). Experience has indicated that the standard deviation of the breakdown stress is 2psi. A random sample of nine specimens is tested, and the average breaking stress observed on them is 98 psi. Should the fiber be considered acceptable with?

Answer 1

To determine if the fiber should be considered acceptable, a hypothesis test is performed. The sample mean breaking stress is 98 psi. The calculated t-value is -3, which is lower than the critical value, leading to the rejection of the null hypothesis.

Step-by-step explanation:

To determine if the fiber should be considered acceptable, we need to perform a hypothesis test. The null hypothesis (H₀) is that the average breaking stress of the fiber is equal to 100 psi, and the alternative hypothesis (H₁) is that the average breaking stress is less than 100 psi. The sample size is 9, and the average breaking stress observed is 98 psi.

We can calculate the test statistic using the formula:

t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))

In this case, the calculated t-value is:

t = (98 - 100) / (2 / sqrt(9)) = -3

Next, we determine the critical value. Since the sample size is small, we can use a t-distribution with n-1 degrees of freedom. With a significance level of 0.05 and 8 degrees of freedom, the critical value is approximately -1.86. Since the calculated t-value (-3) is less than the critical value (-1.86), we reject the null hypothesis.

Therefore, we can conclude that the fiber should be considered acceptable.