Question

In: Statistics and Probability

For each of the following situations, (1) identify the population and sample, (2) explain what µ...

For each of the following situations, (1) identify the population and sample, (2) explain what µ and represent, and (3) decide if the necessary assumptions for constructing a confidence interval are met.

Traffic engineers wanted to know if traffic has increased lately in Clarksville. 200 volunteers installed apps on their mobile phones to track their movements, and the engineers computed the average speed for their commutes to work each day.

A farmer wanted to know how a new fertilizer would affect her corn crop yield. She decides to apply the fertilizer to each of three, one-acre fields, and average the yield across them.

The mean salaries for 14 randomly selected CFOs of Fortune 500 companies were obtained and averaged to estimate the true mean salary for CFOs of all Fortune 500 companies.

The tire pressure was checked and averaged over 94 randomly chosen cars across campus to estimate the average tire pressure in cars driven by people in Montgomery County.

Expert Solution

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.

orchestra answered 2 years ago

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