Question

Here are several situations where there is an incorrect application of the theory underlying tests of significance. Write a short paragraph explaining what is wrong in each situation and why it is wrong. a) A study with x̄ =45 reports statistical significance for Ha: µ > 50. b) A two-sample t statistic gave a P-value of 0.20. From this, we can reject the null hypothesis with 90% confidence if the alternative is one-tailed but not if it is two-tailed. c) Larger sample sizes generally give a larger margin of error for the difference between two sample means. Please be descriptive

Answer 1

a) For the given alternative hypothesis:

09 <11: "H

The null hypothesis is given as:

H, :μ< 50

As we are rejecting the null hypothesis here, this is only possible if the p-value for the test is reasonably small.

We have here:

p= P(t > t*

p = P(+ X -40 SE

p= P(t> 45 – 50 SE?

p= P(t > SF

As the value here is negative, therefore the p-value here would be greater than 0.5, therefore the test can never be significant here. Even for a 90% confidence, the p-value to get the test significant should be less than 0.1.

Therefore the given statement can never be true.

b) For 90% confidence, the null hypothesis is rejected at p - value of less than 1 - 0.9 = 0.1 and not 0.2. Therefore the given statement is false.

c) For the difference in 2 means, the margin of error is computed as:

MOE = z*SE = +

Clearly the margin of error here is proportional to the reciprocal of the square root of the sample size. Therefore the larger sample sizes actually gives us a smaller margin of error and not larger.