Problems related to text's Chapter 7: 1. Assume you need to build a confidence interval for a population mean within some given situation. Naturally, you must determine whether you should use either the t-distribution or the z-distribution or possibly even neither based upon the information known/collected in the situation. Thus, based upon the information provided for each situation below, determine which ( t -, z - or neither) distribution is appropriate. Then if you can use either a t- or z- distribution, give the associated critical value (critical t - or z - score) from that distribution to reach the given confidence level. a. 99% confidence n=150 σ known population data believed to be very skewed Appropriate distribution: Associated critical value: b. 95% confidence n=10 σ unknown population data believed to be normally distributed Appropriate distribution: Associated critical value: c. 90% confidence n=40 σ unknown population data believed to be normally distributed Appropriate distribution: Associated critical value: d. 99% confidence n=12 σ unknown population data believed to be very skewed Appropriate distribution: Associated critical value: 2. A student researcher is interested in determining the average ( µ ) GPA of all FHSU students, in order to investigate grade inflation at regional universities. The data below represent the GPA's of thirty randomly selected FHSU students. 2.75 2.55 3.95 1.74 2.66 3.10 2.41 1.57 2.12 3.67 3.56 1.98 4.00 3.21 1.95 3.75 1.45 3.01 2.29 2.66 3.95 2.50 3.88 2.79 2.32 3.44 2.07 0.62 2.72 3.55 3.92 3.41 2.14 1.15 2.75 3.25 a. How do you know that you will need to construct the confidence interval using a t -distribution approach as opposed to a z -distribution? We want to construct the mean value confidence interval for the GPA's with a 90% confidence level. b. Determine the best point estimate (average) for the mean GPA. c. Determine the critical t -value(s) associated with the 95% confidence level. d. Determine the margin of error. e. Determine the confidence interval. .