Surveys of students’ hours of studying has the following results: a sample of 21 econ students has a mean=25 and a variance =36; a sample of 16 poly sci students has a mean=7 and a variance=85. Are the variance of study hours the same for econ and poly sci students? Use a significance level of .01. The null hypothesis is The alternative hypothesis is the critical value of the test statistics is the value of the test statistic is your conclusion is

Step-by-step explanation:

Hello!

The objective of these surveys is to compare if the population variances of the studying hours of econ students and poly sci students are equal.

To do this analysis you have to conduct a variance ratio test.

Be:

X₁: Time in hours that an economy students studies

n₁: 21 students

X[bar]₁= 25 hs

S₁²= 36 hs

And

X₂: Time in hours that a poly sciences students studies

n₂: 16 students

X[bar]₂= 7 hs

S₂²= 85 hs

The hypotheses are:

H₀: σ₁² = σ₂²

H₁: σ₁² ≠ σ₂²

α: 0.01

The test statistic is a Snedecor's F

This test is two-tailed so the rejection region is divided in two tails:

So, you will reject the null hypothesis if ≤ 0.29 or if ≥ 3.88

And you will not reject the null hypothesis if 0.29 < < 3.88

This value is between 0.29 and 3.88, then the decision is to not reject the null hypothesis.

Using a 1% level of significance, there is no significant evidence to reject the null hypothesis. You can conclude that the population variances of the time the economy and poly science students spend studying are the same.

I hope this helps!

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743