Question

Words were displayed on a computer screen with background colors of red and blue. Results from scores on a test of word recall are given below. Use a 0.05 significance level to test the claim that the samples are from populations with the same standard deviation. Assume that both samples are independent simple random samples from populations having normmal distributions. Does the background color appear to have an effect on the variation of word recall​ scores? n x sRed Background 35 15.14 5.91Blue Background 37 12.42 5.42What are the null and alternative hypotheses?

Answer 1

Answer:

Yes, the background color appear to have an effect on the variation of word recall​ scores

Step-by-step explanation:

Given that results from scores on a test of word recall are given are as follows:

Two test scores have independent means and having normal distribution.

$H_0: Means are equal\\H_a: Means are not equal$

(Two tailed test at 5% significance level)

Group   Group One     Group Two  

Mean    15.1400 12.4200

SD              5.9100 5.4200

SEM     0.9990 0.8910

N                35       37      

The mean of Group One minus Group Two equals 2.7200

standard error of difference = 1.335

Hence t statistic = 2.0369

p value = 0.0454

Since p <0.05 we reject null hypothesis

Yes, the background color appear to have an effect on the variation of word recall​ scores