Answer:
a
The null hypothesis is ![H_o : \sigma^2_1 = \sigma^2 _2](https://tex.z-dn.net/?f=H_o%20%3A%20%20%5Csigma%5E2_1%20%3D%20%5Csigma%5E2%20_2)
The alternative hypothesis is ![H_a : \sigma_1 ^2 > \sigma^2_2](https://tex.z-dn.net/?f=H_a%20%3A%20%20%5Csigma_1%20%5E2%20%3E%20%5Csigma%5E2_2)
b
![F_{critical} = 1.8608](https://tex.z-dn.net/?f=F_%7Bcritical%7D%20%3D%201.8608)
c
![F = 2.9085](https://tex.z-dn.net/?f=F%20%3D%202.9085)
d
The decision rule is
Reject the null hypothesis
e
There is sufficient evidence to support the researchers claim
Step-by-step explanation:
From the question we are told that
The first sample size is ![n_1 = 30](https://tex.z-dn.net/?f=n_1%20%3D%2030)
The sample variance for elementary school is ![s^2_1 = 8324](https://tex.z-dn.net/?f=s%5E2_1%20%3D%208324)
The second sample size is ![n_2 = 30](https://tex.z-dn.net/?f=n_2%20%3D%2030)
The sample variance for the secondary school is ![s^2_2 = 2862](https://tex.z-dn.net/?f=s%5E2_2%20%3D%202862)
The significance level is ![\alpha = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%3D%200.05)
The null hypothesis is ![H_o : \sigma^2_1 = \sigma^2 _2](https://tex.z-dn.net/?f=H_o%20%3A%20%20%5Csigma%5E2_1%20%3D%20%5Csigma%5E2%20_2)
The alternative hypothesis is ![H_a : \sigma_1 ^2 > \sigma^2_2](https://tex.z-dn.net/?f=H_a%20%3A%20%20%5Csigma_1%20%5E2%20%3E%20%5Csigma%5E2_2)
Generally from the F statistics table the critical value of
at first and second degree of freedom
and
is
![F_{critical} = 1.8608](https://tex.z-dn.net/?f=F_%7Bcritical%7D%20%3D%201.8608)
Generally the test statistics is mathematically represented as
![F = \frac{s_1^2 }{s_2^2}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7Bs_1%5E2%20%7D%7Bs_2%5E2%7D)
=> ![F = \frac{8324 }{2862}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B8324%20%7D%7B2862%7D)
=> ![F = 2.9085](https://tex.z-dn.net/?f=F%20%3D%202.9085)
Generally from the value obtained we see that
Hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to support the researchers claim