Question

The five statistics students (n=5) are compared to a sample of 8 sociology students with regard to the number of hour they sleep. Here is the data for hours slept:

8, 6, 5, 13, 10

The mean hours slept for sociology students (n=8) is 7.2 with a standard deviation of 1.7.

Conduct a t-test to determine if the statistics students sleep a different amount than the sample of sociology students?

Be sure to address all four steps of the hypothesis test.

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. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.

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 = 1.5560
DF = 11
t = [ (x₁ - x₂) - d ] / SE

t = 0.7712

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 11 degrees of freedom is more extreme than -0.77; that is, less than -0.77 or greater than 0.77.

Thus, the P-value = 0.458

Interpret results. Since the P-value (0.458) is greater than the significance level (0.05), we have to accept the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that the statistics students sleep a different amount than the sample of sociology students.