Question

To encourage efficiency at a drive through window, a fast food restaurant chain specifies, as a guideline, that at least half of all drive through orders should be taken, prepared, and delivered in 3 minutes or less. Subsequently, a random sample of 64 drive through orders was taken and it was found that 24 of them were taken, prepared and delivered in 3 minutes or less. The remaining orders from the sample took longer than 3 minutes. The fast food company would like to know if they are meeting the specified guideline. Which test should be used?Single sample test of means with unknown variance (standard deviation)Two sample test of proportionsSingle sample test of proportionsTwo sample test of means with unknown variance (standard deviation)

Answer 1

Answer: Single sample test of proportions

Explanation:

Let p be the proportion of drive through orders should be taken, prepared, and delivered in 3 minutes or less.

To encourage efficiency at a drive through window, a fast food restaurant chain specifies, as a guideline, that at least half of all drive through orders should be taken, prepared, and delivered in 3 minutes or less.

i.e. p≥0.50

As per given , we have

`\text{Null hypothesis }H_0: p\geq0.50\\\\ \text{Alternative hypothesis }H_a:p<0.50`

Since the alternative hypothesis is left-tailed , so the test is a one-tailed test of proportions.

Thus , the test should be used : Single sample test of proportions