Confidence Interval for the Difference Between Two Independent Means

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Do boys and girls perform differently on driving tests? To investigate this matter, a researcher selects a simple random sample of $32$ boys $(X_1)$ and girls $(X_2)$ and gives each of them a driving test.

Each student gets a score from $0$ to $100$ . These are their test results:

Boys $(X_1)$

Girls $(X_2)$

$\begin{array}{rcl} n_1 &=& 16\\ \bar{X_1} &=& 73.4\\ s_1 &=& 5.0 \end{array}$

$\begin{array}{rcl} n_2 &=& 16\\ \bar{X_2} &=& 72.0\\ s_2 &=& 3.4 \end{array}$

You may assume that the test scores are approximately normally distributed.

Construct a $97\%$ confidence interval for the difference between the two population means $\mu_1 - \mu_2$ . Round your answers to $3$ decimal places.

$CI_{(\mu_1 - \mu_2),\,97\%}=\,($

$,\,\,\,$

$)$

8. Testing for Differences in Means and Proportions: Independent Samples t-test

Confidence Interval for the Difference Between Two Independent Means