Question

A company is investigating two potential vendors on the timeliness of their deliveries. A random sample of size 10 from the first vendor produced an average delay time of 4.5 days with a standard deviation of 2.3 days. A random sample of size 12 from the second vendor yielded an average delay time of 3.4 days with a standard deviation of 6.2 days. (a) Find a 90% confidence interval for the ratio of the variances of the delay times for the two vendors. (b) Can we conclude that the first vendor has a smaller variability regarding delay times than the second? Use a significance level of 0.05. (c) Which vendor would you select, and why?

Answer 1

(a)

Here we have-

Here, the degree of freedom of numerator is df1=12-1=11, and the degree of freedom for the denominator is df2=10-1=9. Since

So, the critical values are-

So,

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(b)

Hypotheses are-

The test is right-tailed.

Test statistics will be-

Degree of freedoms are- df=12-1=11, df2= 10-1-9

The p-value using excel function "=FDIST(7.267,11,9)" is: 0.0030

Since the p-value is less than 0.05, we reject the null hypothesis. We can conclude that the first vendor has a smaller variability regarding delay times than the second.

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(c)

I would select the first vendor because the first vendor has a smaller variability.