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Answer:
The critical value of <em>F</em> 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:
<em>H₀</em>: The standard deviations are same, i.e. <em>σ</em>₁ = <em>σ</em>₂
<em>Hₐ</em>: The standard deviations are different, i.e. <em>σ</em>₁ > <em>σ</em>₂<em>.</em>
A <em>F</em>-test will be used to perform the hypothesis test.
The <em>F</em>-statistic is given by:
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
<u>Step 1</u>:
Open function → F.INV.RT
A dialog box will open.
<u>Step 2</u>:
Enter the details as shown in the image below. Press OK
Thus, the critical value of <em>F</em> is 3.55.
