1. You have conducted a focus group of 100 customers in order to estimate their willingness-to-pay for a new product. You observed variability among individual willingness-to-pay values of +/- $150,...

1. You have conducted a focus group of100 customers in order to estimate their willingness-to-payfor a new product. You observed variability among individual willingness-to-pay values of +/- $150, andderived a 95% margin of error of roughly+/-$30for your overall estimate of average willingness-to-pay.

Your supervisor wasn't happy with your analysis, and they said: "Look, I need to know to within $10 what the average is that customers are willing to pay. $30 is too large an amount of uncertainty.Go take a new sample of 300 customers. If you have 3 times the data, you should have 3 times the accuracy."

Explainwhy your supervisor's suggestion won't work in the way that they think.

Be specific in your answerconcerning what kind ofsample you'dactuallyneed.

2. Assume you are estimating the average age of a population at 95% confidence with asample size of 144 peopleand knownstandard deviation of 24 years. Calculate the size of the 95%margin of error(the +/-part,not the confidence interval)(#to 2decimal places)

Based on the values above and your calculated margin of error, if you found asample average of32 years, answer whether you would be willing to believe a claim that thetrue average in the populationin questionwas35years.("yes" or "no")

3. A tax preparation firm currently has 3 locations to serve customers: A downtown office location, a location in a suburban mall, and a location in a rural Walmart store. Each location has different foot traffic and customer profiles.

The primary performance metric is average turnaround/processing time for tax returns prepared on site.The descriptive statistics from a sample of tax return preparation from each location are summarized in the table below.

If the firm sampled 25 returns each from the 3 above locations,identify whether we should conclude that the differences among observed average tax preparation time at the 3 locations are substantive and meaningful.

That is, based on the observed mean differences and known/estimated variability in the sampling process, answer whether the observed differences seem more likely to be real or to be simply the result of random sampling.

You do not need to report a specific calculated value, but youmust explain your answerin reference to which statistics would be relevant and what they seem to show.

4. The tax preparation firm described in the previous question gave these performance ratings to 5 employees:

Identify what kind of errorseems to havebeen made in assigning these performance ratings.Briefly explain.

Additionally answer (using appropriate statistics as the basis for your response)what the new ranking order of performance ratings (from lowest to highest) should likely be after the error has been corrected.