Exam 1

  1. Question

    The daily expenses of summer tourists in Vienna are analyzed. A survey with 132132 tourists is conducted. This shows that the tourists spend on average 168.8168.8 EUR. The sample variance sn12s^2_{n-1} is equal to 230.6230.6.

    Determine a 95%95\% confidence interval for the average daily expenses (in EUR) of a tourist.


    1. What is the lower confidence bound?
    2. What is the upper confidence bound?

    Solution

    The 95%95\% confidence interval for the average expenses μ\mu is given by: [y1.96sn12n,y+1.96sn12n]=[168.81.96230.6132,168.8+1.96230.6132]=[166.209,171.391]. \begin{aligned} & & \left[\bar{y} \, - \, 1.96\sqrt{\frac{s_{n-1}^2}{n}}, \; \bar{y} \, + \, 1.96\sqrt{\frac{s_{n-1}^2}{n}}\right] \\ & = & \left[ 168.8 \, - \, 1.96\sqrt{\frac{230.6}{132}}, \; 168.8 \, + \, 1.96\sqrt{\frac{230.6}{132}}\right] \\ & = & \left[166.209, \, 171.391\right]. \end{aligned}


    1. The lower confidence bound is 166.209166.209.
    2. The upper confidence bound is 171.391171.391.