Question

what example can I use when explaining the four requirement s of a differnce of means test?

Answer 1

Ans:

These are the four requirement s of a differnce of means test.

(1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results

(1) state the hypotheses

Every hypothesis test requires the analyst to state a null hypothesis and an alternative hypothesis. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false; and vice versa

The table below shows three sets of null and alternative hypotheses. Each makes a statement about the difference d between the mean of one population μ₁ and the mean of another population μ₂. (In the table, the symbol ≠ means " not equal to ".)

Set	Null hypothesis	Alternative hypothesis	Number of tails
1	μ1 - μ2 = d	μ1 - μ2 ≠ d	2
2	μ1 - μ2> d	μ1 - μ2 < d	1
3	μ1 - μ2< d	μ1 - μ2 > d	1

(2) formulate an analysis plan

The analysis plan describes how to use sample data to accept or reject the null hypothesis. It should specify the following elements.

• Significance level. Often, researchers choose significance levels equal to 0.01, 0.05, or 0.10; but any value between 0 and 1 can be used.
• Test method. Use the two-sample t-test to determine whether the difference between means found in the sample is significantly different from the hypothesized difference between mean

(3) analyze sample data

Using sample data, find the standard error, degrees of freedom, test statistic, and the P-value associated with the test statistic.

• Standard error. Compute the standard error (SE) of the sampling distribution.

  SE = sqrt[ (s₁²/n₁) + (s₂²/n₂) ]

  where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is the size of sample 1, and n₂ is the size of sample 2.
• Degrees of freedom. The degrees of freedom (DF) is:

  DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }

  If DF does not compute to an integer, round it off to the nearest whole number. Some texts suggest that the degrees of freedom can be approximated by the smaller of n₁ - 1 and n₂ - 1; but the above formula gives better results.
• Test statistic. The test statistic is a t statistic (t) defined by the following equation.

  t = [ (x₁ - x₂) - d ] / SE

  where x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
• P-value. The P-value is the probability of observing a sample statistic as extreme as the test statistic. Since the test statistic is a t statistic, use the t Distribution Calculator to assess the probability associated with the t statistic, having the degrees of freedom computed above. (See sample problems at the end of this lesson for examples of how this is done.)

(4) interpret results

If the sample findings are unlikely, given the null hypothesis, the researcher rejects the null hypothesis. Typically, this involves comparing the P-value to the significance level, and rejecting the null hypothesis when the P-value is less than the significance level.