The following information is available for two samples selected from independent
ID: 3151027 • Letter: T
Question
The following information is available for two samples selected from independent normally distributed populations Complete parts (a) and (b) Population A: n = 16 S^2 = 50 2 Population B n = 21 S^2 = 15 6 At the 0 05 level of significance is there evidence of a difference between sigma_1^2 and sigma_2^2? Determine the hypotheses Choose the correct answer below H_0: sigma_1^2 notequalto sigma_2^2 H_1: sigma_1^2 = sigma_2^2 H_0: sigma_1^2 lessthanequalto sigma_2^2 H_1: sigma_1^2 > sigma_2^2 H_0: sigma_1^2 = sigma_2^2 H_1: sigma_1^2 notequalto sigma_2^2 H_0: sigma_1^2 greaterthanorequalto sigma_2^2 H_1: sigma_1^2 sigma_2^2? What is your statistical decision? The upper-tail critical value of F is (Round to two decimal places as needed ) What is your statistical decision? H_0. There is evidence that sigma_1^2 > sigma_2^2.Explanation / Answer
a) Option C)
b) To obtain test statistic, go to Minitab>Basic statistics>2-sample variance and enter sample size and variances corresponding to Sample 1 and Sample 2. Click Ok.
Fstat=3.22
p value:0.016
Reject H0. There is sufficient evidence to conclude difference exists between two variances. [P value is less than 0.05]
b) at DF1=15, and DF2=20, the upper tail critical valu eis around 2.86.
Reject H0: There is sufficient evidence to conclude variance of sample1 is greater than sample2. [The test statistic falls in critical region]
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