In: Statistics and Probability
a)
1. Population is all the commutes in Clarksville
Sample is commutes that are being used by 200 volunteers.
2. Mu is the average speed of all the commutes in Clarksville.
3. Here the assumption of randomization is not met for constructing confidence interval. Since all the 200 volunteers are selected but there is no mention that these volunteers are randomly selected or not.
b)
1.population is the fertilizers of all the 3 fields.
Sample, here no sample is being selected since the farmer is applying the fertilizers to each of the 3 fields.
2. Mu is the average yield of crops after applying the fertilizer.
3. Here the entire population is selected for applying the fertilizer. There is no sample. Confidence intervals are only for sample.
c)
1. population is all the CFOs of 500 Fortune company.
Sample is14 selected CFOs.
2. Mu is the mean salary of all the CFOs of 500 Fortune company.
3. Here the conditions of randomization, independence, 10% condition is satisfied. Thus we can construct confidence interval. But note that the sample size is 14 so the population must be normally distributed.
d)
1. Population is all the cars driven by people in Montgomery Country.
Sample is 94 randomly chosen cars.
2. Mu is the average tire pressure of all the cars in Montgomery Country.
3. Here the conditions of randomization, independence is met. The population can be assumed to be 10 times larger than the sample size of 94. Sample size 94 is quite large to apply central limit theorem. Thus confidence interval can be constructed since all the conditions are met.