Question

Using the Excel sheet for Constructing Confidence Intervals, answer the following questions.

1.   Construct a 90% confidence interval for the true mean of a normal population if a random sample size of 40 from the population yields a sample mean of 75 and the population has a standard deviation of 5.

Lower limit: ______________     upper limit: ______________

2. A random sample, consisting of the values listed below, was taken from a normally distributed population. Assuming the standard deviation of the population is unknown, construct a 99% confidence interval for the population mean.

Table for 2
27.4	26.5	25.7	31.4
28.2	21.9	16.3	22.7
18.8	34.4	29.2	20.5

Lower limit: ______________     upper limit: ______________

Answer 1

1)

Sample size = n = 40

Sample mean = = 75

Population standard deviation = = 5

We have to construct 90% confidenc interval for the population mean.

Here population standard deviation is known so we have to use one sample z-confidence interval.

z confidence interval

Here E is a margin of error

Zc = 1.645   ( Using z table)

So confidence interval is ( 75 - 1.3004 , 75 + 1.3004) = > ( 73.6996 , 76.3004)

Using excel