4. Researchers investigated whether cell phone use impairs driver’s reaction tim

Question

4. Researchers investigated whether cell phone use impairs driver’s reaction times, using a sample of 64 students from the University of Utah. Students were randomly assigned to a cell phone group or to a control group. The experiment measured each subject’s mean response time over many trials. The sample sizes, the sample means, and the sample standard deviations for the two groups are given below. Group n Mean Standard deviation Cell Phone 31 573.1(milliseconds) 58.9 Control 32 533.7(milliseconds) 65.3 The data showed no strong outliers or strong skewness, so the researchers decided to use the two-sample t procedures. (a) Calculate a 95% confidence interval for the mean difference between these two independent groups. (b) Which group has higher mean response time? Explain why? show steps

Explanation / Answer

HEre as the data given here

As we can see that there are standard deviation has not much differnces so we will use t - test for two sample mean with equal variances.

Here pooled standard deviation sp = sqrt [(n1 -1)s12 + (n2 -1)s22 ) / (n1 + n2 -2)]

sp = sqrt [ (30 * 58.92 + 31 * 65.32 )/ 61] = 62.235

95% confidence interval for the mean difference between these two independent groups

= (xmobile - xcontrol) +- tn1 +n2 -2 , 0.05 [sp * sqrt (1/n1 + 1/n2)]

= (573.1 - 533.7) +- t61,0.05 * 62.235 * sqrt(1/31 + 1/32)

= 39.4 +- 2.000 * 62.235 * 0.252

= 39.4 +- 31.3674

= (8.0326, 70.7674)

(b) Here we can see that there is no zero involved in the confidence interval so we can say that the group cellphone is abosultely have higher mean than the group control. So, we can conlude that Cellphone group has higher mean resonse time.

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