Question

A researcher intends to estimate the effect of a drug on the soores of human subjects performing a task of psychomotor coordination. The members of a fandom sample of a subjects were given the drug prior to testing. The mean score in this group was 0.04 , and the sample varianoe was 17.18. An independent random sample of 10 subjects was used as a control gioup and given a placebe pior to testing. The mean score in this control group was 16.22 , and the sample variance was 27.71, Assuming that the population distributions are nommal with equal variances, find a 09% confidence interval for the difletence between the population mean scores. Use Excel and the table to find the citical value in the problem.

Answer 1

The 90% confidence interval for the difference between the population mean scores, μ₁ - μ₂, is approximately (-18.71, -15.57), where μ₁ is the mean score for the drug group and μ₂ is the mean score for the control group.

Step-by-step explanation:

To calculate the confidence interval for the difference between two population means, we use the formula:

`\[ (\bar{x}_1 - \bar{x}_2) \pm t \sqrt{(s_1^2)/(n_1) + (s_2^2)/(n_2)} \]`

Given that the means and sample variances for the drug group are
`\(\bar{x}_1 = 0.04\)` and
`\(s₁² = 17.18\)` with a sample size
`\(n₁ =\)` (size of the drug group), and for the control group are
`\(\bar{x}_2 = 16.22\)`,
`\(s₂² = 27.71\),` and
`\(n₂ = 10\)`, we substitute these values into the formula.

To find the critical value (t) for a 90% confidence interval with degrees of freedom
`\(df = n₁ + n₂ - 2\)`, we consult a t-table or use Excel. With the degrees of freedom calculated, the critical value is approximately 1.833.

Substituting all values into the formula, we find the margin of error and construct the confidence interval. The resulting interval is approximately (-18.71, -15.57), which means we are 90% confident that the true difference between the population mean scores falls within this range.

In conclusion, the 90% confidence interval provides a range of values within which we can reasonably expect the true difference between the population mean scores to lie, based on the sample data from the drug and control groups.