Question

1. A social science researcher collected data from a random sample of 400 students at a large university and found that, on average, they belonged to 2.6 campus organizations. The standard deviation σ for the population is 1.8.

1. Using these data, construct a 95% confidence interval for µ, the mean number of campus organizations belonged to by the population of students at this university.

2. Write a sentence to interpret your confidence interval, making sure to provide all the important information.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     =2.6

Population standard deviation =    = 1.8

Sample size n =400

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 1.8/ 400 )

= 0.1764
At 95% confidence interval estimate of the population mean
is,

- E < < + E

2.6-0.1764 <   < 2.6 + 0.1764

2.4236<   < 2.7764

( 2.4236,2.7764)

At 95% confidence interval estimate of the population mean
is,
( 2.4236,2.7764)