Part 1 (a) What is the point estimate of µ ? µ = (b) Find corresponding to a 95%
ID: 3360228 • Letter: P
Question
Part 1
(a) What is the point estimate of µ?
µ =
(b) Find corresponding to a 95% confidence level.
=
(c) Find 1 /2.
1 /2 =
(d) Find z/2 for 95% confidence level.
z/2 =
2.
Round your answer up to the nearest whole number.
2.
Part 1
For a data set obtained from a sample of size n = 64 with = 44.25, it is known that = 4.4.
(a) What is the point estimate of µ?
(b) Find z score corresponding to a 95% confidence level, z/2. Recall that (1 )100% = 95%.
(c) Construct a 95% confidence interval for µ.
(d) What is the margin of error in part (c)?
Recall the following definitions from section 8.2-3 of the text.
The confidence level is denoted by (1 – )100%, where is called the significance level. = P(|Z| > z). By symmetry, /2 = P(Z > z).
The endpoints for a (1 – )100%, confidence interval for , if is known and either the population is normal or n 30, are given by
where the value of z is obtained from the standard normal distribution (Table IV in Appendix C or by calculator) and is the standard deviation of
The quantity is called the Margin of Error and is denoted by E.
To obtain z from a graphing calculator we use the formula z = invNorm(1 /2, µ, ) where µ is the mean and is the standard deviation of the normal distribution. For standard normal distribution µ = 0 and = 1.
Recall that in general z = invNorm("area to left of z", µ, )
Explanation / Answer
Mean is 44.25 and s is 4.4 and N is 64. thus standard error is SE=(4.4)/sqrt(64)=0.55
a) point estimate of mean is 44.25
b) z for 95% confidence is 1.96
c) lower limit is mean-z*SE=44.25-0.55*1.96=43.172
upper limit is mean+z*SE=44.25+0.55*1.96=45.328
d) margin of error is z*SE =0.55*1.96 =1.078