Answer:
There is no sufficient evidence to support the claim that men and women differ in repeatability for this assembly task
Step-by-step explanation:
Given
Let subscript 1 represent men and 2 represent women, respectively.
![n_1 = 25](https://tex.z-dn.net/?f=n_1%20%3D%2025)
![n_2 = 21](https://tex.z-dn.net/?f=n_2%20%3D%2021)
![s_1 = 0.98](https://tex.z-dn.net/?f=s_1%20%3D%200.98)
![s_2 = 1.02](https://tex.z-dn.net/?f=s_2%20%3D%201.02)
![\alpha = 0.02](https://tex.z-dn.net/?f=%5Calpha%20%3D%200.02)
Required
Determine if here is enough evidence
First, we need to state the hypotheses
![H_o: \sigma_1^2 = \sigma_2^2](https://tex.z-dn.net/?f=H_o%3A%20%5Csigma_1%5E2%20%3D%20%5Csigma_2%5E2)
![H_1: \sigma_1^2 \ne \sigma_2^2](https://tex.z-dn.net/?f=H_1%3A%20%5Csigma_1%5E2%20%5Cne%20%5Csigma_2%5E2)
Next, calculate the test statistic using:
![F = \frac{s_1^2}{s_2^2}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7Bs_1%5E2%7D%7Bs_2%5E2%7D)
![F = \frac{0.98^2}{1.02^2}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B0.98%5E2%7D%7B1.02%5E2%7D)
![F = 0.923](https://tex.z-dn.net/?f=F%20%3D%200.923)
Calculate the rejection region;
But first, calculate the degrees of freedom
![df_1 =n_1 - 1](https://tex.z-dn.net/?f=df_1%20%3Dn_1%20-%201)
![df_1 =25 - 1](https://tex.z-dn.net/?f=df_1%20%3D25%20-%201)
![df_1 =24](https://tex.z-dn.net/?f=df_1%20%3D24)
![df_2 = n_2 -1](https://tex.z-dn.net/?f=df_2%20%3D%20n_2%20-1)
![df_2 = 21 - 1](https://tex.z-dn.net/?f=df_2%20%3D%2021%20-%201)
![df_2 = 20](https://tex.z-dn.net/?f=df_2%20%3D%2020)
Using the F Distribution: table
![c = \frac{\alpha}{2}](https://tex.z-dn.net/?f=c%20%3D%20%5Cfrac%7B%5Calpha%7D%7B2%7D)
![c = \frac{0.02}{2}](https://tex.z-dn.net/?f=c%20%3D%20%5Cfrac%7B0.02%7D%7B2%7D)
![c = 0.01](https://tex.z-dn.net/?f=c%20%3D%200.01)
At 0.01 level (check row 20 and column 24), the critical value is:
<em></em>
<em> --- the upper bound</em>
At 0.01 level (check row 24 and column 20), the critical value is:
![f_{0.01,20,24} = 2.74](https://tex.z-dn.net/?f=f_%7B0.01%2C20%2C24%7D%20%3D%202.74)
Calculate the inverse F distribution.
---- the lower bound
The rejection region is then represented as:
![0.365 < Test\ Statistic < 2.86](https://tex.z-dn.net/?f=0.365%20%3C%20Test%5C%20Statistic%20%3C%202.86)
If the test statistic falls within this region, then the null hypothesis is rejected
--- Test Statistic
![0.365 < 0.923 < 2.86](https://tex.z-dn.net/?f=0.365%20%3C%200.923%20%3C%202.86)
<em>The above inequality is true; so, the null hypothesis is rejected.</em>
<em>This implies that, there is no sufficient evidence.</em>