Question

Students in a statistics class are conducting a survey to estimate the mean number of units students at their college are enrolled in. The students collect a random sample of 47 students. The mean of the sample is 12.3 units. The sample has a standard deviation of 1.9 units.What is the 95% confidence interval for the average number of units that students in their college are enrolled in? Assume that the distribution of individual student enrollment units at this college is approximately normal.(____,______)Your answer should be rounded to 2 decimal places.

Answer 1

Answer:

(11.76, 12.84)

Step-by-step explanation:

Given that we can assume that the distribution of individual student enrollment units at this college is approximately normal.

Sample mean =12.3

sample std dev s = 1.9 units

Sample size = 47

Std error = $\frac{1.9}{\sqrt{47} } \\=0.277$

Z critical value for 95% = 1.96

Margin of error = $1.96*0.277=0.543$

Confidence interval =

$(12.3-0.543, 12.3+0.543)\\= (11.757, 12.843)$

=(11.76, 12.84)