F-Distributions and Its Applications

The given operators are tested for their efficiency in terms of number of units produced per day by five different types of machines.

State null hypothesis and alternative hypothesis.

Test at $5\%$ level of significance whether the operators and the machines differ in terms of their efficiency? 

A farmer applies three types of fertilizers on four separate plots. The figures on yield per acre are tabulated below.

Test whether there is any significant difference among mean yields of different plots and among different fertilizers and test the hypothesis.

The following data refer to the yield of wheat in quintals on plots of equal area in two agricultural blocks $A$ and $B$.

Is the variance of yield for block A is greater than that of block B at $5\%$ level of significance.(Answer $H_0$ is rejected/not rejected)

A test was given to five students taken at random from $\mathrm{XI}$ class of three schools of a town. The individual scores are

Carry out the one-way ANOVA. (Answer $H_0$ is rejected/not rejected)

Check whether the  $H_0$ is rejected/not rejected.

A sample of $7$ observations, the sum of the squares of deviations of the sample values from its sample mean was $74.4$. In another sample of $11$ observations it was $100.6$. Test whether the two population variances are equal at $5\%$ level.

A home gardener wishes to determine the effects of four fertilizers on the average number of tomatoes produced. Test at $5\%$ level of significance the hypothesis that the fertilizers $A$, $B$, $C$ and $D$ have equal average yields. 

Three processes $X$, $Y$ and $Z$ are tested to see whether their outputs are equivalent. The following observations on outputs were made.

Carry out the one-way analysis of variance and state your conclusion.

A test was given to five students taken at random from $XII$ class of three schools of a town. The individual scores are

Carry out the one-way ANOVA. (Answer $H_0$ is rejected/not rejected)

A farmer applies three types of fertilizers on four separate plots. The figures on yield per acre are tabulated below.

Test whether there is any significant difference among mean yields of different plots and among different fertilizers and test the hypothesis.

The given operators are tested for their efficiency in terms of number of units produced per day by five different types of machines.

State null hypothesis and alternative hypothesis.

Test at $5\%$ level of significance whether the operators and the machines differ in terms of their efficiency? 

For test of significance for two normal population variance, find the test statistic value of given data.

Sample I: $n_1=10$, $\sum (x_i-\overline{x}{)}^2=90$, sample II:  $n_2=17$,$\sum (y_i-\overline{y}{)}^2=64$.

For test of significance for two normal population variance, $s_x^2=30$ and $s_y^2=20$. Find the test statistic value for the given data.

For test of significance for two normal population variance, $s_x^2=60$ and $s_y^2=50$. Find the test statistic value for the given data.

For test of significance for two normal population variance, a sample I of $n_1=11$ observations, the sum of the squares of deviations of the sample values from its sample mean was $\sum (x_i-\overline{x}{)}^2=50$. In another sample II of $n_2=21$ observations it was $\sum (y_i-\overline{y}{)}^2=200$. Find the test statistic value of given data.

For test of significance for two normal population variance, a sample I of $n_1=8$ observations, the sum of the squares of deviations of the sample values from its sample mean was $\sum (x_i-\overline{x}{)}^2=84.4$. In another sample II of $n_2=10$ observations it was $\sum (y_i-\overline{y}{)}^2=102.6$. Find the test statistic value of given data.

Find population variance for the following data:

$\sum _{i=1}^N{\left(x_i-\mu \right)}^2=300, N=20$

Find population variance for the following data:

$\sum _{i=1}^N{\left(x_i-\mu \right)}^2=250, N=10$

Find population variance for the following data:

$\sum _{i=1}^N{\left(x_i-\mu \right)}^2=100, N=5$

Difference between population variance and sample variance.

Define population variance?