2. Consider the following scenario You are a researcher studying the effects of

Question

2. Consider the following scenario You are a researcher studying the effects of drinking water on health. The 200 residents of Phonyville drink water from a local aquifer that is known to be higher in minerals, some of which are known to be beneficial, and some of which may be harmful. Your working/alternate hypothesis (Ha) s that the number of sick days taken by Phonoille residents will be different from the statewide average. The null hypothesis (Ho) is that the number of sick days taken by working residents of Phonyvile will be the same as the statewide average. Fortunately, you know the mean and standard deviation values for the number of sick days for the population of the state. You will collect data on all 200 working residents of Phonvville for the purposes of the study a) In this scenario, which is the sample, and which is the population? b) You choose a confidence level of 95%, what is the -value (significance level) associated with this confidence level? c) Given this significance level, what are the chances that any completely random sample of 200 workers in the state would have a mean that is significantly different from the statewide average (i.e., different from the population mean)? d) Would you run a z-test or a t-test? e) Your observed test statistic (t or z observed) is 2.43. Your critical statistic is 1.96. Will you reject the null hypothesis? f) Based on your assessment and your confidence level, what are the chances you committed a Type I error? What, then are the chances (expressed as a percentage) that the mean number of sick days taken by residents of Phonyville is "really" different from the statewide average and not just a random anomaly? g) If you instead did probability testing and found a p-value of 0.03, what would be the chances (%) that the Fake City and statewide means are truly different?

Explanation / Answer

a)

Population: Total population of working residennts in Phonyville

sample: the 200 working residents in  Phonyville

b)

Significance level is 100-95 = 5%

c)

Given the significance level, there is 5% chance that the sample means us different from the mean

d)

We know the SD of population. So we use z test.

e) Test statistic is greater than critical value. So we reject Ho.

f)

Type I error is nothing but the significance level. i.e. 5%

g) Probability is p-value i.e. 3%

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