Question

A random sample of 225 first year statistics students were selected and the number of student absences in a semester were recorded. The results were an average number of11:6 absences with a standard deviation of 4:1 absences. Estimate the mean number of absences per semester with a 90% confidence interval.

a. Write down the formula you intend to use (with variable notation).

b. Write down the above formula with numeric values replacing the symbols.

c. Write down the confidence interval in interval notation.

Answer 1

a. Write down the formula you intend to use (with variable notation).

The required formula is given as below:

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Sample mean = Xbar = 11.6

Sample standard deviation = S = 4.1

Sample size = n = 225

Degrees of freedom = df = n – 1 = 224

Confidence level = 90%

Critical t value = 1.6517

(by using t-table)

Part b

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 11.6 ± 1.6517*4.1/sqrt(225)

Confidence interval = 11.6 ± 1.6517*0.273333333

Confidence interval = 11.6 ± 0.4515

Lower limit = 11.6 - 0.4515 = 11.15

Upper limit = 11.6 + 0.4515 = 12.05

Part c

Confidence interval = (11.15, 12.05)

11.15 < µ < 12.05