A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a population standard deviation of 6 hours, what is the required sample size if the error should be less than ½ hour with a 95% level of confidence?
95% = mean ± 1.96 SEm
SEm = SD/√n
130
To determine the required sample size for a given level of confidence and maximum error, you can use the formula:
n = ((Z * σ) / E)²
where:
n = required sample size
Z = z-score corresponding to the desired level of confidence (in this case, 95% confidence corresponds to a z-score of approximately 1.96)
σ = population standard deviation
E = maximum acceptable error
In this case, the population standard deviation (σ) is given as 6 hours and the maximum error (E) is less than ½ hour, which can be written as 0.5 hours.
Plugging in the given values, the formula becomes:
n = ((1.96 * 6) / 0.5)²
n = (11.76 / 0.5)²
n = 23.52²
n ≈ 554.70
Since the sample size should be an integer, round up to the nearest whole number.
Therefore, the required sample size is 555 students.