Question

MS 304.. Saved milton burse File Home Insert Draw Desig Layou Refere Mailin Revies View Help O Tel me Be caref PROTECTED VIEW 6 Problem 6: (3 points) Suppose a machine produces metal sheets that are specified to be 22 milimeters thick Because of the machine, the operator, the raw material, the manufacturing environment, and other factors, there is variability in the thickness. Two machines produce these sheets. Operators are concerned about the of the two machines. To test consistency, they randomly sample 10 sheets produced by machine 1 and 12 sheets produced by machine 2. The thickness measurements of sheets from each machine are given in the table below. Assume sheet thickness is normally distributed in the population. How can we test to determine whether the variance from each sample comes fiom the same population variance (population variances are equal) or from different population variances (population variances are not equal)? Machine 1 223 219 218 224 223 225 216 222 218 216 S 0.11378 220 21.7 221 219 218 220 219 221 222 219 220 221 si-0.1 2023

Answer 1

Solution:-

6)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis H₀: σ₁² = σ₂²

Alternative hypothesis H_A: σ₁²$\neq$ σ₂²

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data. Using sample data, the degrees of freedom (DF), and the test statistic (F).

DF₁ = n₁ - 1 = 10 -1

D.F₁ = 9

DF₂ = n₂ - 1 = 12 -1

D.F₂ = 11

Test statistics:-

$F = \frac{s_{1}^{2}}{s_{2}^{2}}$

F = 0.9464

Since the first sample had the smaller standard deviation, this is a left-tailed test.

p value for the F distribution = 0.9464

Interpret results. Since the P-value (0.475) is greater than the significance level (0.05), we have to accept the null hypothesis.

From the above test there is sufficient evidence to conclude that each sample comes from same population variance.