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Question 1 of 1 - / 1 View Policies Current Attempt in Progress The mean breaking strength of a ceramic insulator must be at least 10 psi. The process by which this insulator is manufactured must show equivalence to this standard. If the process can manufacture insulators with a mean breaking strength of at least 94 psl, it will be considered equivalent to the standard. A random sample of 50 insulators is available, and the sample mean and standard deviation of breaking strength are 9.20 psi and 0.21 psi, respectively. a. State the appropriate hypotheses that must be tested to demonstrate equivalence. H:]; H: Edit b. What are your conclusions using a = 0.05? There is enough evidence to conclude that the process by which the insulators are manufactured is equivalent to the stand... is not e Textbook and Media Save for Later Attempts: 0 of 3 used Submit Answer

Answer 1

Solution:

Given:

From the data, sample mean is
r
= 9.20 and the Sample standard deviation is s = 0.21

The sample size is n = 50.

a) Null and Alternative Hypotheses:

Η : μ29.4 Η :μ<9.4

This corresponds to a left-tail test, for which a t-test for one mean, with unknown population standard deviation will be used.

Test statistic:

Formula: iu t= Calculation: 9.20-9.4 t =-6.734 0.21/ 50 t= -6.734

The number of degrees of freedom are df = n-1 = 50-1 = 49

Rejection Region:
Given significance level = α = 0.05 and df = 49
So Critical Value for the test is, tc = -1.677   …Using excel formula, =TINV(2*(1-0.05),49)

Decision:

Since it is observed that |t| = 6.734> |tc| = 1.677
It is then concluded that the Null Hypothesis is rejected.

b) Conclusion: There is not enough evidence to conclude that the process by which the insulator are manufactured is equivalent to the standard.

Done