Question

How many students should be sampled if you want to estimate the true mean number of credit hours per student with an error of no more than 0.7 with 95% confidence. From a prior study, it is known that the standard deviation is 1.5.

Answer 1

To estimate the mean number of credit hours per student with a margin of error of 0.7 and 95% confidence, we need to sample at least 18 students, assuming a known population standard deviation of 1.5.

Step-by-step explanation:

To estimate the true mean number of credit hours per student with an error of no more than 0.7 with 95% confidence, we need to use the formula for the sample size of a mean which is:

n = (Z*σ/E)^2

Where n is the sample size, Z is the Z-value associated with the confidence level, σ is the population standard deviation, and E is the margin of error.

For a 95% confidence level, Z is approximately 1.96 (from the Z-table). Given that the population standard deviation (σ) is 1.5, and the margin of error (E) is 0.7, the sample size calculation is as follows:

n = (1.96 * 1.5 / 0.7)^2

Calculating this gives:

n = (2.94 / 0.7)^2

n = (4.2)^2

n = 17.64

Since sample size cannot be a fraction, we would round up to the nearest whole number. Therefore, the required sample size would be 18 students.