Q1. During 9 surveys throughout the past decade, the apartment vacancy rates in Minneapolis (in percentage) were found to be 4.9, 6.3, 5.7, 4.4, 3.0, 3.6, 3.8, 6.1, and 4.5, respectively. Assume that the measurements represent a random sample from a normal population, find a 95% prediction interval for the apartment vacancy rate in Minneapolis during the next survey.
Q2. In St. Paul, the annual unemployment rates (in percentage) during the years 1995-2000 are:
3.6, 3.9, 3.2, 2.9, 3.0, 3.1
And the annual unemployment rates during the years 2006-2011 are:
4.3, 4.7, 5.5,8.3, 7.7, 7.5
Comment on the evidence available concerning equality of the variances of the unemploy¬ment rates for St. Paul during the two periods.
Q3. On August 26, 2011, Metro Transit reported that 13% of the Vikings fans travel to Metrodome on the Hiawatha light-rail line. To test this claim, we randomly ask 10 Viking fans whether they travel to Metrodome on the Hiawatha line. If 1 or more fans answered yes, we shall not reject the null hypothesis that p = 0.13; otherwise, we conclude that p < 0.13.
(a) Evaluate α, assuming that p = 0.13.
(b) Evaluate β for the alternative p = 0.06.
Q4. During the past 10 years, Minnesota Pollution Control Agency has measured the concentration of chlorophyll-a in Lake Calhoun 64 times. The mean concentration 2' was 3.6 parts per billion (ppb). It is known that the standard deviation σ was 1.6 ppb.
Is this a firm evidence that the the mean concentration of chlorophyll-a in Lake Calhoun is greater than 3.0 ppb? Answer your question by computing Pr(X‾ > 3.6 | μ= 3.0). Assume that the distribution of chlorophyll-a concentration is normal.