(Solved): 1. (3 pts) What are \( \pi, \mu, \sigma^{2} \) stand for and what are their point estimates for con ...

1. (3 pts) What are \( \pi, \mu, \sigma^{2} \) stand for and what are their point estimates for confidence interval estimations? 2 (6 pts) Find the values of the critical points \( z \) and \( t \) in the following (Remember that sample size is needed for the critical point \( t \) ): (a) \( n=23 \) and confidence level is \( 95 \% \). (b) \( n=17 \) and confidence level is \( 98 \% \). 3 (3 pts) What is a suggested formula for \( e \) in the following confidence interval estimate where \( p \) represents a sample proportion: \[ (p-\epsilon, p+c) \] 4.(3 pts) A sample of size 80 which found to contain 21 smokers. What is the sample proportion of non-smokers in this sample? 5 (5 pts) A survey of 499 women for the American Orthopedic Foot and Ankle Society revealed that \( \% 37 \) wear flats to work. Find \( 99 \% \) confidence interval for the population proportion of women who wear flats to work. 6 (5 pts) A poll of size 30 in a huge shopping mall found that 23 women wish to have an attraction area for kids in the mall. Determine the sample size that is required to estimate the population proportion of women who wish to have an attraction area, with errors of \( \pm 0.05 \) and \( 99 \% \) confidence level. Values of \( t \) for Selected Probabilities Standard Normal Distribution Table