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 49 students. The mean of the sample is 12.2 units. The standard deviation is 1.6 units. What is the 95% confidence interval for the number of units students in their college are enrolled in? Assume that the distribution of individual student enrollment units at this college is approximately normal.

Answer 1

( 11.7 , 12.7 )

Explanation:

The provided information is:

Sample mean =
`\bar{X} = 12.2`

Standard deviation =
`\sigma=1.6`

Sample size = n = 49

Significance level =
`\alpha=0.05`

Thus, the 95% confidence interval is:

`\bar{X}\pm Z_(\alpha/2)(\sigma)/(√(n))\\=12.2\pm Z_(0.05/2)(1.6)/(√(49))\\=12.2\pm 1.96*0.2286\\=12.2\pm 0.4480\\=(11.7.12.7)`