Question

Consider the normal population with an unknown population standard deviation. A random sample results in xbar= 64.54 and s^2=46.24

a) construct the 90% confidence interval for mu if xbar and s^2 were obtained from a sample of 23 observations( round intermediate calculations to at least 4 decimal places. Sample mean and sample standard deviation to 2 decimal places and t value to 3 decimals and final answer to 2 decimals)

b) construct the 90% confidence interval for mu if xbar and s^2 were obtained from a sample of 27 observations( round intermediate calculations to at least 4 decimal places. Sample mean and sample standard deviation to 2 decimal places and t value to 3 decimals and final answer to 2 decimals)

c) what is the impact of the sample size on the width of the interval does it

-lead to a larger interval width and is more precise interval

OR

smaller interval width  and more precise interval

Answer 1

The standard deviation of the sample is

a)

(b)

(c)

Larger sample size leads to smaller interval width  and more precise interval.