Suppose a marine biologist was studying a population of lobsters

Instructions: Please show all formulas and calculations in an organized fashion for full credit.

Problem 1.Suppose a marine biologist was studying a population of lobsters of the coast of

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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% condence, what is the margin of error?

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

c. Briey explain the effect of having a larger sample size bigger than 10 on the margin of error and condence 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% condence interval for the percentage of the public that feel that sports have a positive e
ect on society.

b. At 95% condence, nd the smallest sample size needed to obtain the mostconser-vativecondence interval with a margin of error of 0.01.