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In: Statistics and Probability

A popular online retail website was interested in consumer spending during the holiday shopping weekend after...

A popular online retail website was interested in consumer spending during the holiday shopping weekend after Thanksgiving. They collect data on a random sample of 400 shoppers, particularly noting how much money each shopper spent. The following histogram was constructed using the data:

The retailer determines that this sample had an average of $84.71 with a standard deviation of $46.87.

  1. (1 point) What is the best point estimate for the true mean amount of money spent by all shoppers at this website during the weekend after Thanksgiving?
  2. (3 points) Are the conditions for constructing a confidence interval satisfied? Be sure to comment on each condition individually.
  3. (3 points) Find the margin of error for a 98% confidence interval estimate for the true mean spending.
  4. (2 points) Construct a 98% confidence interval estimate for the true mean spending.
  5. (1 point) Interpret the interval in the context of the data. Your answer should reference what “98% confidence” means and how the two endpoints of the interval relate to the estimate.
  6. (2 points) Last year, shoppers spent an average of $82.24 on this website. The company uses their sample data to claim that the average consumer spending has increased this year. Based on the confidence interval, is this claim justified? Why or why not?
  7. (1 point) Without doing any calculation, explain why a 95% confidence interval would be a narrower interval than the one you computed in part (d).
  8. (2 points) How would the confidence interval be affected if the sample was of size 800 instead of 400? Explain briefly without calculating the new confidence interval.

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Expert Solution

orchestra answered 1 year ago
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