Question

In: Statistics and Probability

Problem 3 You hypothesize that people who drive sports cars have faster reaction times than those...

Problem 3

You hypothesize that people who drive sports cars have faster reaction times than those who drive nonsports cars (e.g., sedans, pickup trucks, etc.). You design a task that measures response time to detect a visual target presented on a screen for 500 ms. The two types of drivers completed 300 trials of the task and the mean reaction times were calculated. The data are shown on the right. Did you find support for your hypothesis?

Use the four-step hypothesis testing procedure described in class, formatted as in the sample assignment. In addition, calculate 1) the effect size and 2) confidence interval associated with the data. Show your work.

Mean reaction times
sports car drivers	nonsports car drivers
556	592
542	560
544	415
490	509
480	412
503	570
463	470
477	509
493	469
576	458
596	534
496	460
559	574
568	518
583	598
451	509
401	549
501	526
599	575
490	467
449	447
508	559
401	581
418	460
413	496
586	515
423	486
428	403
586	590
594	564
414	445
528	594
459	432
559	439
442	500

Expert Solution

Two-Sample T-Test and CI: sports car drivers, nonsports car drivers

Method

μ₁: mean of sports car drivers

µ₂: mean of nonsports car drivers

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
sports car drivers	35	502.2	64.0	11
nonsports car drivers	35	508.1	58.9	10

Estimation for Difference

test statistic

confidence interval =

Difference	95% Lower Bound for Difference
-6.0	-30.5

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ > 0

T-Value	DF	P-Value
-0.41	67	0.657

since p-value is greater than level of significance hence we fail to reject the null hypothesis and we conclude that there is significant evidence that people who drive sports cars have faster reaction times than those who drive nonsports cars.

cohens-d (effect size)

Cohen's d = (M₂ - M₁) ⁄ SD_pooled

SD_pooled = √((SD₁² + SD₂²) ⁄ 2)

Cohen's d = (508.1 - 502.2) ⁄ 61.502886 = 0.09593.

orchestra answered 2 years ago

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