Question

THE SAMPLE STATISTICS ARE GIVEN BELOW. ASSUME THE POPULATION VARIANCES ARE NOT EQUAL USE a=0.01

n1=18 n2=13

X1= 785 X2=770

S1=40 S2=25

PLEASE NOTE THAT THE X'S HAVE A BAR OVER THEM

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 u₂

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. 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 = 11.7032
DF = 12
t = [ (x₁ - x₂) - d ] / SE

t = 1.282

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 12 degrees of freedom is more extreme than -1.282; that is, less than -1.282 or greater than 1.282.

Thus, the P-value = 0.224.

Interpret results. Since the P-value (0.224) is greater than the significance level (0.01), we have to accept the null hypothesis.