Question

A new string is being manufactured by "strings are us". The company wishes to test a hypothesis about the string's strength. It is known that the population standard deviation is 1.1 and using a sample of 20 specimens, it was found that the average was 9.5. a. Test the hypothesis that the mean strength of the string is less than 10. Use a=0.07

Answer 1

Let denotes the mean strength of the string.

Thus, we have to test, H0: = 10 against H1: < 10.

The test-statistic is given by, Z = , where, = 9.5,

= 10, = 1.1, n = 20.

Hence Z = - 2.0328.

Under H0, Z ~ N(0,1).

p-value = P(Z < - 2.0328) = (-2.0328) = 0.021.

Since, p-value = 0.021 < level of significance = 0.07,

we reject H0.

We conclude that there is significant evidence to claim that

the mean strength of the string is less than 10 units.