1. The Mill Valley Brewery distributes beer in bottles labeled as 32oz, and claims their standard deviation to be 0.75oz. The Bureau of Weights and Measures randomly selects 50 of these bottles, measures their contents, and obtains a sample mean of 31.8oz.

a) What is the sampling distribution of xbar, and how do you know that?

b) Assuming the beer is properly filled as labeled, how likely was it to have gotten a mean of 31.8 from their sample? Using a 0.01 significance level, test the Bureau's claim that the brewery is cheating their consumers. What is...

c) ...the null hypothesis?

d) ...the alternative hypothesis?

e) ...the test statistic?

f) ...the critical value?

g) ...the result of the significance test? Note: BE THOROUGH. Do NOT just answer Reject or Fail to Reject.

2.

Many people believe that the moon influences the actions of some individuals. A study of dementia patients in nursing homes recorded various types of disruptive behaviors every day for 12 weeks. Days were classified as moon days if they were in a 3-day period centered at the day of the full moon. For each patient, the average number of disruptive behaviors was computed for moon days and for all other days. The hypothesis is that moon days will lead to more disruptive behavior. The data is a follows: Patient Moon Days Other Days |Difference 3.33 0.27 3.06 3.67 0.59 3.08 2.67 0.32 2.351 3.33 0.19 3.14 3.33 1.26 2.07 3.67 0.11 3.56 4.67 0.3 4.37 2.67 0.4 2.27 1.59 4.41 4.33 0.6 3.73 3.33 0.65 2.68 0.67 0.69 -0.02 1.33 1.26 0.07 0.33 0.23 0.1 0.38 1.62 The following EXCEL output is provided: Moon Days Other Days Mierence Mean 3.022 Mean 0.589333333 Mean 2.432660667 Standard Error 1.386981235 Standard Error 0.114872462 Standard Error 0.377053068 Mediar 8.33 Median Median 2168 Mode 3.33 Mode 6 Mode #NIA Standard Deviation 1.498771878 Standard Deviation | 0.444899132] 2 Standard Deviation 1.460320252 Sample Variance 2.246317143 Sample Variance 0.197935238 Sample Variance 2.132535238 Kurtosis 1.189526931 Kurtosis 0.517112402 Kurtosis 0.584033447 Skewnes! -0.115869713 Skewness 1.21114287 Skewnest -0.574806385 Range 5.67 Range 1.48 Range Minimum 0.33 Minimum D.11 Minimum -0102 Maximum 6 Maximum 1.59 Maximum 4.4 Sum 45.33 Sum 8.84 Sum 16.49 Count 5 Count 15 Count 15