A meal delivery company had a standard deviation of 2.52.5 minutes in delivery times under its old logistics system. After switching to a new route optimization algorithm, the company recorded the following delivery times (in minutes) for a simple random sample of 1212 deliveries:31.2,30.9,32.1,29.8,31.5,30.2,32.7,31.0,30.6,31.9,30.7,31.331.2, 30.9, 32.1, 29.8, 31.5, 30.2, 32.7, 31.0, 30.6, 31.9, 30.7, 31.3At the 0.050.05 significance level, test the claim that the new system results in less variation in delivery times than the old system (i.e., the standard deviation is less than 2.52.5 minutes).

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Problem 50Multiple Choice

A meal delivery company had a standard deviation of $2.5$ minutes in delivery times under its old logistics system. After switching to a new route optimization algorithm, the company recorded the following delivery times (in minutes) for a simple random sample of $12$ deliveries:
$31.2 comma 30.9 comma 32.1 comma 29.8 comma 31.5 comma 30.2 comma 32.7 comma 31.0 comma 30.6 comma 31.9 comma 30.7 comma 31.3$
At the $0.05$ significance level, test the claim that the new system results in less variation in delivery times than the old system (i.e., the standard deviation is less than $2.5$ minutes).

Fail to reject the null hypothesis. There is not enough evidence to support the claim that the new system has less variation.

Reject the null hypothesis. There is enough evidence to support the claim that the new system reduces variation in delivery times.

Reject the null hypothesis. The variation in delivery times is greater under the new system.

Fail to reject the null hypothesis. The new system increases the variation in delivery times.

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