Suppose the typical lifespan of a type of chain used in industry was believed to

Question

Suppose the typical lifespan of a type of chain used in industry was believed to have mean =20months. A sample of the last n=15worn out chains yielded a sample mean of x(bar)=21.14. Assuming that the chain life is normally distributed with known standard deviation =4, conduct a hypothesis test that the mean lifespan of the chains has changed. Do this by assuming a signicance level =0.05 and calculating the p-value below. Please write your answer to three decimal places.

Can someone help me calculate the p-value with this given information?

Explanation / Answer

Null HYpothesis : H0 : Lifespan of chain =20 months

ALternative Hypothesis : Ha : Lifespan of chain 20 months

Test Statisitic

as population standard deviation is known we will use Z - test

Z = (xbar - H)/ (/n) = (21.14 - 20)/ (4/15) = (1.14)/ (1.0328) = 1.104

so, no we have to calculate the p- value.

p - value is the probability of getting sample mean equal or more than the given sample mean 21.14 months. As it is a two directional test we will multiplyit two times.

so p - vlaue = 2* Pr( xbar >21.14; 20; 4/15 ) = 2 (1 -   (1.104) )

where   is the cumulative normal standard distribution function

p - vlaue = 2 * Pr( xbar >21.14; 20; 4/15 ) = 2(1 -   (1.104)) = 2 * 0.1348 = 0.2696

so , we cannot reject the null hypothesis and chains typical lifespan is 20 months.

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