Question

The mean score on a biology exam taken by all undergraduate students in a college in a particular year is 67.8 with a standard deviation of 11.5. The standard error of the mean for a sample of 70 students is , and the margin of error of the mean is . (Round off your answers to the nearest hundredth.)

Answer 1

In this question we simple wish to calculate the standard error and margin of error from the population. This can be done purely using the standard deviation and sample size.

Standard error
= std dev / (SQRT) n
= 11.5 / SQRT of 70
= 11.5 / 8.366
= 1.374

Margin of error is the standard error multiplied by a Z value that correspondence to a confidence percentage. At a 95% confidence the Z value is 1.96. Therefore
MOE = 1.96 x 1.374 = 2.69

Answer 2

The standard error of the mean for a sample of 70 students is 1.375 .

The margin of error of the mean is 2.69 .

[Round off your answers to the nearest hundredth]