Question

Two boxes each have a lot of numbers in them. The means and the standart deviations of the boxes are equal. A sample of 45 is taken from the first box and a sample of 55 taken from the second. If it is claimed that the first box has a higher mean, what is the probability that based on the samples, a hypothesis test at significance 0.0025 will not support the claim? ( use z table preferably)

Answer 1

Solution:- The probability that based on the samples, a hypothesis test at significance 0.0025 will not support the claim is 0.9975.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁< u₂
Alternative hypothesis: u₁ > u₂ (Claim)

Note that these hypotheses constitute a one-tailed test.  

Any probability greater than 0.0025, we have to accept the null hypothesis and we will not be able to support the claim.

So the required probability = 1 - 0.0025 = 0.9975