Question

Suppose a company manufactures ropes that are known to, on average, break when sup-

porting 75kg. An engineer claims that her ropes are superior (have a higher break point),

but they also cost substantially more to manufacture.

In the context of a hypothesis test, we would make the following assumption about the new rope Ho: μ = 75 and look for evidence of her claim Ha : μ > 75. Let’s assume σ is known to be 9 for the new ropes. We can think of that hypothesis test as a proxy for deciding whether to start manufacturing the new ropes. Consider the alternative value μ = 76, which in the context of the problem would presumably not be a practically significant departure from Ho — that is, given the extra cost of the ropes, the relatively small increase in average durability is not worth it. Also, from an individual rope standpoint (with a standard deviation of 9kg) the durability increase would not be noticeable to a consumer.

(a) For an α level .01 test, compute β at this alternative for sample sizes n = 100, 900, and 2500.

(b) If the observed mean of is x = 76, what can you say about the resulting p-value when n = 2500? Is the data statistically significant at any of the standard values of α?

(c) Would you want to use a sample size of 2500 along with a level α=.01 test (disregard the cost of running the experiment)? Explain.

Answer 1