A manager of a grocery store wants to determine if consumers are spending more than the national average of $150 with a standard deviation of $30. The manager collects 10 random receipts and finds that the average customer spends $160. He then concludes that his customers do spend more than the national average. a) What do you see as his error in this assumption? b) How could you redesign the study to correct it?

Question

Mathematics

Gregory

9 March, 10:16

A manager of a grocery store wants to determine if consumers are spending more than the national average of $150 with a standard deviation of $30. The manager collects 10 random receipts and finds that the average customer spends $160. He then concludes that his customers do spend more than the national average. a) What do you see as his error in this assumption? b) How could you redesign the study to correct it?

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Blaine White · Answer 1

A.) The manager calculated mean and not standard deviation

B.) Standard deviation should be calculated with the use of formula.

Step-by-step explanation:

A.) The assumption that his customers do spend more than the national average is wrong because the standard deviation is not calculated and mean cannot be used as a substitute for standard deviation.

B.) Standard deviation tells us how value obtain from group measurement deviates from the average value or expected value of each item of observations.

When standard deviation is low, this show that the value is very close to the expected value or the average value.

If the national average value = $150 and average customer spends $160.

Deviation = 160 - 150 = 10

This is lower than $30

Or better still, the manager should make use of standard deviation formula. Which is the square root of variance.