checking of correctness of excel program for F test i would like to express my doubt about  F test performed by Analysis toolpak , let us consider following link
F Test in excel 
everything seems  ok until calculation of one tail critical value, generally for two tailed test alpha is divided into 2, in this case $\alpha=0.05$ and  its half would bee  $\alpha/2=0.025$(both left and right right) and for two tailed test  right   critical value is taken, because Df  are  5 and 4, in excel critical value for right part would be
=F.INV.RT(0.025,5,4)

which is  equal to  9.364470816, but  excel give us value 6.256056502, which is simple critical value for right  tail test , not  two tailed test, it  can be verified by  following command
=F.INV.RT(0.05,5,4)

am i right? i think that excel program does not support two tailed test right?
 A: Right-sided alternative: The sample variance for females is $S_f^2 = 160$ and the
sample variance for males is $S_m^2 = 21.7.$
In R, the test of $H_0: \sigma_f^2/\sigma_m^2 = 1$ against $H_a: \sigma_f^2/\sigma_m^2 > 1$ gives the following result.
f = c(26,25,43,34,18,52);  m = c(23,30,18,25,28)
var.test(f, m, alt="g")   # 'g' for 'greater'

        F test to compare two variances

data:  f and m
F = 7.3733, num df = 5, denom df = 4, p-value = 0.03789
alternative hypothesis: true ratio of variances is greater than 1
95 percent confidence interval:
 1.178581      Inf
sample estimates:
ratio of variances 
          7.373272 

P-value as rejection criterion: So even though sample sizes are small, the sample variance for females is
sufficiently larger than the sample variance for males to reject $H_0$ at the
5% level; the P-value is 0.038 < 0.05.
This P-value can be computed in R as follows:
1 - pf(7.3733, 5, 4)
[1] 0.03788813

Critical value as rejection criterion: The 5% critical value for this one-sided test is the number $c$ such that $P(F > c) = 0.95,$ so that $c = 6.2561.$ Using this critical value, we reject $H_0$ because the observed variance ratio $7.3733 > 6.2561.$
qf(.95, 5, 4)
[1] 6.256057

A plot of the density function of the distribution $\mathsf{F}(5,4)$ is shown below. The observed variance ratio is at the vertical blue line. The P-value
of the one-sided test is the area beneath the density curve to right of this line. The critical value $c=6.2521$ is shown by the vertical red dotted line; the are to the right of this line is $0.05.$

Using software, it is more common to use the P-value of the test, rejecting
$H_0$ at the 5% level, if the P-value is less than 5%. 
Two-sided alternative: If you are doing a two-sided test, it is customary to double the applicable P-value. (In this case
that's the P-value for the right-sided test because the variance ratio exceeds 1.) Then the two-sided P-value is taken to be $2(0.03789) = 0.07578,$ so you would not reject
doing a two-sided test. [Because the F-distribution is not symmetrical, it would be hard to say what value below 0 would be 'as extreme as' 7.373272.]
In R, the P-value for a two-sided test agrees with this value. The output is
shown below, slightly abbreviated.
var.test(f, m, alt="t")   # 't' for 'two-sided'

        F test to compare two variances

data:  f and m
F = 7.3733, num df = 5, denom df = 4, p-value = 0.07578
alternative hypothesis: true ratio of variances is not equal to 1
...

Critical values for two-sided test: Below is the density function of $\mathsf{F}(4,5)$ with dotted red lines
(at $0.1354$ and $9.3645$)
cutting off probability 0.025 from each tail of the distribution.

Notice that the variance ratio (heavy blue line) is between the two
critical values; accordingly, $H_0$ is not rejected against the two-sided alternative.
A: If you read the example link carefully, even without any calculation, they are just inconsistent, switching from two tail to one tail ...
They started with two-tailed hypotheses: "H1: σ21≠σ22"
Then calculates the right-tailed test.
Finally, finished with the conclusion of the right-tailed test: "Conclusion: if F > FCritical one-tail, we reject the null hypothesis. This is the case, 7.373 > 6.256."
