A fast food restaurant that sells burritos is concerned about the variability in the amount of filling that different employees place in the burritos. To achieve product consistency it needs this variability to be no more than 1.7 ounces. A sample of n = 18 burritos showed a sample variance of 2.89 ounces. Using a 0.10 level of significance, what can you conclude? A) The standards are being met since (test statistic) (critical value). C) The standards are being met since (test statistic) (critical value). D) The standards are not being met since (test statistic)

Question

A fast food restaurant that sells burritos is concerned about the variability in the amount of filling that different employees place in the burritos. To achieve product consistency it needs this variability to be no more than 1.7 ounces. A sample of n = 18 burritos showed a sample variance of 2.89 ounces. Using a 0.10 level of significance, what can you conclude? A) The standards are being met since (test statistic) < (critical value). B) The standards are not being met since (test statistic) > (critical value). C) The standards are being met since (test statistic) > (critical value). D) The standards are not being met since (test statistic) < (critical value).

Quizplus · Accepted Answer

To test if the variability in the amount of filling exceeds 1.7 ounces, we use the chi-square test for variance. The null hypothesis $H_0$ would state that the population variance $\sigma^2$ is less than or equal to 1.7 ounces^2, and the alternative hypothesis $H_a$ would state that the population variance is greater than 1.7 ounces^2. The test statistic is calculated using the formula $\chi^2 = \frac{(n-1)s^2}{\sigma_0^2}$, where $n$ is the sample size, $s^2$ is the sample variance, and $\sigma_0^2$ is the variance under the null hypothesis. Given $n = 18$ and $s^2 = 2.89$, and testing against $\sigma_0^2 = 1.7$, the test statistic would be greater than the critical value at the 0.10 level of significance, indicating that the null hypothesis should be rejected. This means the variability in the amount of filling is significantly greater than the standard allows, hence the standards are not being met.

A Fast Food Restaurant That Sells Burritos Is Concerned About