Answer :
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:
[tex]F=\frac{S_{1}^{2}}{S_{2}^{2}}\sim F_{\alpha/2, (n_{1}-1),(n_{2}-1)[/tex]
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.
In this exercise we have to use the knowledge of functions to calculate the ciritic value that will correspond to:
The critical value of F is 3.55.
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:
- [tex]H_0[/tex]: The standard deviations are same: [tex]\sigma_1\ = \sigma_2[/tex]
- [tex]H_a[/tex]: The standard deviations are different: [tex]\sigma_1 > \sigma_2[/tex]
A F-test will be used to perform the hypothesis test. The F-statistic is given by:
[tex]F=\frac{S_1^2}{S_2^2}= F_{\alpha/2}, (n_1-1)(n_2-1)[/tex]
The information provided is we have :
[tex]Sample \ mean\\\\Sample \ Standard \ Deviation\\\\Sample \ size[/tex] [tex]University A\\\\1104\\\\134\\\\14[/tex] [tex]University B\\\\1254\\\\108\\\\8[/tex]
Compute the critical value of F using MS-Excel as follows, the degrees of freedom are:
[tex]df_1 = n_1 - 1 = 14 - 1 = 13\\df_2 = n_2 - 1 = 8 - 1 = 7[/tex]
Now it will be necessary to follow a few steps and observe the given image:
- Open function → F.INV.RT
- A dialog box will open.
- Enter the details as shown in the image below. Press OK
- Thus, the critical value of F is 3.55.
See more about critical value at brainly.com/question/5425085
