Question

The following observations are from two independent random samples, drawn from normally distributed populations. Sample 1 9.74, 9.04, 8.06, 6.09, 7.51 Sample 2 |[25.96, 26,27, 26,34, 39.09, 33.88, 28.87, 33.46] We are interested in testing the null hypothesis that the two population variances are equal, against the one-sided alternative that the variance of Population 1 is larger than the variance of Population 2. Define Population 1 to be the population with the larger sample variance a) What are the appropriate null and alternative hypotheses? b) What is the value of the Ftest statistic? Round your response to at least 3 decimal places. Number c) What conclusion can be made at the 5% level of significance? There is insufficicent evidence to reject the null hypothesis at the 5% level of significance, and therefore no significant evidence that the population variances are not equal to each other There is sufficient evidence to reject the null hypothesis at the 5% level of significance, and therefore evidence that the variance of Population 1 is larger than the variance of Population 2.

Answer 1

Ans:

Population 1	Population 2
25.96	9.74
26.27	9.04
26.34	8.06
39.09	6.09
33.88	7.51
28.87
33.46
5.0402	1.4109

a)

Option 3 is correct.

$H_0:\sigma _1^2=\sigma _2^2$

$H_a:\sigma _1^2>\sigma _2^2$

b)

F statistic=5.0402^2/1.4109^2=12.762

df1=7-1=6

df2=5-1=4

p-value=FDIST(12.762,6,4)=0.0138

c)As,p-value<0.05,we reject the null hypothesis.

second option is correct.

There is sufficient evidece to reject the null hypothesis at 5% significance level,and therefore evidence that the variance of population 1 is greater than variance of population 2.