Question

The breaking strengths of cables produced by a certain manufacturer have a mean, u, of 1925 pounds, and a standard deviation of 60 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 32 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1940 pounds. Assume that the population is normally distributed. Can we support, at the level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.) Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.)

H0

H1

The type of statistic

Value of the test statistic

The p-value

Answer 1

Answer

we want to test whether the mean breaking strength has increased or not. So, it is a right tailed hypothesis

we will use z test statistic because the sample size is greater than 30 and population standard deviation is known

test statistic z =

where x = 1940, mu = 1925, sigma = 60 and n= 32

(1.414 is rounded to 3 decimals and 1.41 is rounded to 2 decimals)

using the z value in z distribution, check 1.4 in the left most column and 0.01 in the top row, then select the intersecting cell, we get

p value = 0.0787 (rounded to 4 decimals)