Question

Perform a hypothesis test (comparing means) on the two populations below. Assume equal means and normal distribution.

Population A	Population B
42	65
41	22
50	51
25	17
78	24
35	57
19	67
22	26
45	88
45	85

Answer 1

Solution:-

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

Null hypothesis: u₁ = u ₂
Alternative hypothesis: u₁ u ₂

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 9.984
DF = 18
t = [ (x₁ - x₂) - d ] / SE

t = - 1.0

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is the size of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.

Since we have a two-tailed test, the P-value is the probability that a t statistic having 18 degrees of freedom is more extreme than -1.00; that is, less than -1.00 or greater than 1.00.

Thus, the P-value = 0.331

Interpret results. Since the P-value (0.331) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that the two population means are same.