Question

Chapter 08, Section 8.2, Intelligent Tutoring Problem 011 For a data set obtained from a sample of size n-81 with x-47.75, it is known that ?-5.6. (a) what is the point estimate of ?? (b) Find z score corresponding to a 95% confidence level, zo/2. Recall that (1-a)100%-95%. (c) Construct a 95% confidence interval for ?. (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, ? = PIZI > z). By symmetry, a/2 = P(Z > z) The endpoints for a (1-?)100%, confidence interval foru, if ? is known and either the population is normal or n 30, are given 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 x. The quantity Zox 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-a/2, ?, ?) where ? is the mean and ? is the standard deviation of the normal distribution. For standard normal distribution ?-0 and ?-1. Recall that in general z-invNorm("area to left of z", ?, ?)

Answer 1

Ans:

a)Point estimate for $\mu$ =$\bar{x}$ =47.75

b)alpha=1-0.95=0.05

c)1-(alpha/2)=1-(0.05)/2=1-0.025=0.975

d)$z_{\alpha /2}$

normsinv(0.975)=1.96