Question

A market research firm studied the waiting time to order drinks during breakfast time at drive-thru in two coffee shop chains. For a sample of 30 locations of chain A, the sample standard deviation of waiting time was 21.2 seconds, and for a sample of 28 locations of chain B, the sample standard deviation was 31.4 seconds. Do these data suggest that the waiting time is more consistent in chain A

Answer 1

The waiting time is more consistent in chain A compared to chain B.

Step-by-step explanation:

The question is asking whether the waiting time is more consistent in chain A compared to chain B. To determine this, we need to compare the sample standard deviations of the waiting time for both chains. In this case, the sample standard deviation for chain A is 21.2 seconds and for chain B it is 31.4 seconds.

A smaller sample standard deviation indicates less variation in the data, which means the waiting time is more consistent. Therefore, since the sample standard deviation of chain A (21.2 seconds) is smaller than that of chain B (31.4 seconds), we can conclude that the waiting time is more consistent in chain A.

Answer 2

Yes

Step-by-step explanation:

Given that :

CHAIN A:

Sample size n1 = 30

Sample standard deviation of waiting time s1 = 21.2

CHAIN B:

Sample size, n2 = 28

Sample standard deviation of waiting time s2 = 31.4

Null hypothesis H0: s1 = s2

Alternative hypothesis H1: s1 < s2

Test statistic ; Ftest : s1² / s2²

Ftest = 21.2^2 / 31.4^2

= 0.4558399

P value from F statistic : = 0.02 (using p value calculator)

Since the pval < 0.05

Then we reject the Null ; Chain A waiting time is more consistent