Suppose you are interested in determining if the average amount of money that students spend on food at your university per day is greater than $30. You randomly choose 25 students from your campus and calculate that the mean amount of money spent per day is $18.01 with a standard deviation of $2.22. What is the standard error of the mean?

Question

Ryan

Mathematics

6 January, 16:02

Suppose you are interested in determining if the average amount of money that students spend on food at your university per day is greater than $30. You randomly choose 25 students from your campus and calculate that the mean amount of money spent per day is $18.01 with a standard deviation of $2.22. What is the standard error of the mean?

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Jett Friedman · Answer 1

The standard error of the mean is 0.444

Step-by-step explanation:

1. Let's review the information given to us for solving the question:

Size of the sample = 25

Mean amount of money spent per day = US$ 18.01

Standard deviation = US$ 2.22

2. For finding the standard error of the mean, we use the following formula:

Standard error = Standard deviation / √Size of the sample

Standard error = 2.22 / √25

Standard error = 2.22 / 5

Standard error = 0.444

3. Interpretation of the standard error:

The standard error is "the standard deviation of the population of values of a sample statistic in a repeated sampling or its estimate".

Thus, the potential for error in the reported result is not more than ± 0.444 (68% confidence) or no more than 1.96 times the standard error (0.444) = ± 0.87 (at 95% confidence).