Question

QUESTION A new type of rope has a mean breaking strength of 10 kilograms with a standard deviation of 1 kilogram. To test the hypothesis, a random sample of 20 lines are tested and the average breaking strength is found to be 8.5 kilograms. (a) Test the hypothesis, at the 0.01 level of significane the the mean is that - 10 kilograms against the alternative that p < 10 kilograms. (b) Evaluate the P value of the test. т т т т Paragraph Arial 3 120 - T-

Answer 1

a) Find the value of the test statistic z. -μο The value of the test statistic z = Vñ 8.5-10 20 = -6.71 :. test statistic = z = -6.71

Now we have to find the critical value for a significance level = a = 0.01. Required probability = a = 0.01. Find z such that P(Z = z) = 0.01 From standard normal table z = -2.33 (Or) Use excel formula: =NORM.S.INV(0.01) critical region for a significance level a 0.01 is :z< -2.33 .. Reject H, in favour of Hy if the computed value of the statistic is less than -2.33.

Now we have to write the conclusion. We reject the null hypothesis if the test statistic z is in the critical region of a hypothesis test. In our problem, the test statistic z = -6.71(< -2.33) is n the critical region of a hypothesis test. Reject H. If we reject Ho, there is sufficient evidence to support the claim. Conclusion: :: There is sufficient evidence to support the claim that the population mean is lower than 10 kilograms.

b) Now find the p-value. p-value = P(Z < -6.71) = 0.0000 :. p - value = 0.0000

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