Question

It is believed that the SAT scores for students entering two state universities may have different standard deviations. Specifically, it is believed that the standard deviation at University A is greater than the standard deviation at University B. To test this using an alpha = 0.05 level, a sample of 14 student SAT scores from University A was selected and a sample of 8 SAT scores from University B was selected. The following sample results were observed: University A University B = 1104 = 1254 s = 134 s = 108 Based on this information, what is the critical value that will be used to test the hypothesis? Question 22 options: = 3.55 z = 1.645 = 2.832 = 3.237

Answer 1

Answer:

The critical value of F is 3.55.

Step-by-step explanation:

The claim to be test is, the SAT scores for students entering two state universities may have different standard deviations. It is believed that the standard deviation at University A is greater than the standard deviation at University B.

The hypothesis for the test can be defined as:

H₀: The standard deviations are same, i.e. σ₁ = σ₂

Hₐ: The standard deviations are different, i.e. σ₁ > σ₂.

A F-test will be used to perform the hypothesis test.

The F-statistic is given by:

$F=\frac{S_{1}^{2}}{S_{2}^{2}}\sim F_{\alpha/2, (n_{1}-1),(n_{2}-1)$

The information provided is:

                                            University A University B

Sample mean                                   1104               1254

Sample Standard Deviation             134                108

Sample size                                      14                           8

Compute the critical value of F using MS-Excel as follows:

The degrees of freedom are:

df₁ = n₁ - 1 = 14 - 1 = 13

df₂ = n₂ - 1 = 8 - 1 = 7

Step 1:

Open function → F.INV.RT

A dialog box will open.

Step 2:

Enter the details as shown in the image below. Press OK

Thus, the critical value of F is 3.55.