To determine how talking on a cell phone affects driving ability, a researcher s

Question

To determine how talking on a cell phone affects driving ability, a researcher set up an experiment where she measured the reaction times (in milliseconds) of a sample of 12 adults under two conditions. Each participant was measured in a driving simulator while talking on a cell phone and then again without distraction. The order was randomized, and the results are displayed below: a. Assuming normality, construct a 95% confidence interval for the true mean difference of reaction time with and without distraction. b. Is there evidence that talking on a cell phone while driving increases reaction time? Explain why or why not.

Explanation / Answer

Below are the null and alternate hypothesis
H0: d <= 0
H1: d > 0

This is right tailed test, we need to calculate only upper limit i.e. limit at the right side of the curve.

Here dbar = 34.5
sd(bar) = 56.56 (I am getting this value different as per my calculation, but for the calculation purpose I am using the given value)

For 95%, t-value for 19 degrees of freedom = 1.729

upper one side limit = 34.5 + 1.729*56.56/sqrt(12) = 62.7302

(b)

if we perform the hypothesis test for the null hypothesis stated above, we have below result

We consider the results for 1 tailed test only, as we see p-value is greater than significance level of 0.05, we fail to reject the null hypothesis. This means there is no significant evidence that talking on a cell phone while driving increases reation time.

t-Test: Two-Sample Assuming Unequal Variances Sample 1 Sample 2 Mean 529.8333 564.3333333 Variance 2019.242 4722.242424 Observations 12 12 Hypothesized Mean Difference 0 df 19 t Stat -1.45557 P(T<=t) one-tail 0.080919 t Critical one-tail 1.729133 P(T<=t) two-tail 0.161837 t Critical two-tail 2.093024

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