Question

Tool mols Help Mode - Delay - O Independent random samples of parts manufactured by two suppliers show the following results: Supplier Sample Sample size Variance Durham 41 3.8 Raleigh 31 2.0 A firm currently using the Durham supplier will continue to do so unless it can be shown that the Raleigh supplier provides a significantly lower variance in part sizes. Using a level of significance of 0.05, provide a recommendation regarding whether or not the firm should change suppliers. -

Answer 1

Solution:

The null and alternative hypotheses are:

$H_{0}: \sigma^{2}_{Durham}=\sigma^{2}_{Raleigh}$

$H_{a}: \sigma^{2}_{Durham}>\sigma^{2}_{Raleigh}$

Under the null hypothesis, the test statistic is:

$F= \frac{s^{2}_{Durham}}{s^{2}_{Raleigh}}$

$=\frac{3.8}{2.0}$

$=1.9$

The p-value is:

$\boldsymbol{p-value=P(F>1.9)=0.0354}$

The excel function to find the p-value is:

$\\ =FDIST(1.9,40,30) \\ Where \\ 1.9 \is \ the \ test \ statistic \\ 40 \ is \ the \ numerator \ df \\ 30 \ is \ the \ denominator \ df$

Conclusion: Since the p-value is less than the significance level 0.05, we, therefore, reject the null hypothesis and conclude that there is sufficient evidence that Raleigh supplier provides a significantly lower variance in part size at the 0.05 significance level. Therefore, we would recommend the firm to change the supplier