Question

. A researcher took a random sample of 600 college students and surveyed them about how many days of class they missed per semester. On average, the sample missed 3.1 days of class. If the sample standard deviation is .45, construct a confidence interval to estimate the true population mean at the 95% confidence level (.05 alpha level). Make sure to interpret your results in a sentence or two! (HINT: Make sure you use the correct formula for this question, keep in mind that you do not know the population standard deviation.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 3.1 days

sample standard deviation = s = 0.45 days

sample size = n = 600

Degrees of freedom = df = n - 1 = 600 - 1 = 599

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t0.025,599 = 1.964

Margin of error = E = t/2,df * (s /n)

= 1.964 * (0.45 / 600)

Margin of error = E = 0.04

The 95% confidence interval estimate of the population mean is,

- E < < + E

3.1 - 0.04 < < 3.1 + 0.04

( 3.06 < < 3.14 )

We are 95% confident that the true mean of them about how many days of class they missed per semester between 3.06 and 3.14 days.