Question

What approach always results in a smaller, absolute value for z-statistic? options: none of these options use a stronger manipulation, which produces larger group differences use less error-prone measures, which decreases variability use larger sample sizes

Answer 1

Solution:

Generally there are two approaches for making a absolute value for z-statistic.

1. Rejection region approach.

2. p-value(or probability value) approach.

Test statistic: The sample statistic one uses to either reject H_o (and conclude H_a) or not to reject H_o.

Critical values: The values of the test statistic that separate the rejection and non-rejection regions.

Rejection region: the set of values for the test statistic that leads to rejection of H_o.

Non-rejection region: the set of values not in the rejection region that leads to non-rejection of H_o.

P-value: The p-value (or probability value) is the probability that the test statistic equals the observed value or a more extreme value under the assumption that the null hypthothesis is true.

Steps in conducting a Hypothesis Test

Step 1. Check the conditions necessary to run the selected test and select the hypotheses for that test.:

1. If Z-test for one proportion: np0?5 and n(1?p0)?5
2. If a t-test for one mean: either the data comes from an approximately normal distribution or the sample size is at least 30. If neither, then the data is not heavily skewed and without outliers.

   Step 2. Decide on the significance level, ?.

   Step 3. Compute the value of the test statistic:

   If One Proportion Z-test: Z?=p^?p0p0(1?p0)?n

   If One Mean t-test: t?=x¯??0S/?n