UCSB PSTAT 109 Statistics for Economics Question-Quiz 8

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Problem 1

 

 

 

Suppose a marine biologist was studying a population of lobsters off the coast of

 

Singapore. To determine the mean carapace length of this lobster population, she decided to sample 10 of these lobsters and measure their length. She recorded a sample mean carapace length of 60.8mm with standard deviation of 7.97mm.

 

 

 

a. At 99% confidence, what is the margin of error?

 

 

 

b. What is the 99% confidence interval estimate of the population mean carapace length?

 

 

 

c. Briefly explain the effect of having a larger sample size bigger than 10 on the margin

 

 

 

of error and confidence interval estimate you found in parts (a) and (b).

 

 

 

Problem 2

 

 

 

Most Americans love participating in or at least watching sporting events.

 

Some feel that sports have more than just entertainment value. In a survey of 1000 adults, conducted by KRC Research & Consulting, 78% felt that spectator sports have a positive effect on society.

 

 

 

a. Find a 95% confidence interval for the percentage of the public that feel that sports

 

have a positive effect on society.

 

 

 

b. At 95% confidence, find the smallest sample size needed to obtain the most conser-vative confidence interval with a margin of error of 0.01.

 

 

 

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