Question

An observational study of teams fishing for the red spiny lobster in a certain body of water was conducted and the results published in a science magazine. One of the variables of interest was the average distance separating trapsminuscalled ​"trap ​spacing"minusdeployed by the same team of fishermen. Trap spacing measurements​ (in meters) for a sample of seven teams of fishermen are shown in the accompanying table. Of interest is the mean trap spacing for the population of red spiny lobster fishermen fishing in this body of water. Complete parts a through f below.

data: 93, 99,106,95,80,72,86

a. Identify the target parameter for this study. The target parameter for this study is mu .

b. Compute a point estimate of the target parameter. 89.57 ​(Round to two decimal places as​ needed.)

c. What is the problem with using the normal​ (z) statistic to find a confidence interval for the target​ parameter?

A. The point estimate is too large to determine an accurate​ z-statistic.

B. The point estimate is too large to determine an accurate critical value.

C. The sample is small and the trap spacing population has unknown distribution and standard deviation. Your answer is correct.

D. The​ z-statistic is used for confidence intervals for​ proportions, not means.

d. Find a​ 95% confidence interval for the target parameter. left parenthesis nothing comma nothing right parenthesis ​(Round to one decimal place as​ needed.)

e. Give a practical interpretation of the​ interval, part d. Choose the correct answer below.

A. One can be​ 95% confident the true mean trap spacing distance lies within the above interval. This is the correct answer.

B. One can be​ 95% confident the true mean trap spacing distance lies at the mean of the above interval.

C. There is a​ 95% probability that the true mean trap spacing distance is the mean of the interval. Your answer is not correct.

D. One can be​ 95% confident the true mean trap spacing distance is one of the end points of the above interval.

f. What conditions must be satisfied for the​ interval, part d​, to be​ valid? Select all that apply.

A. The population has a relative frequency distribution that is approximately normal. Your answer is correct.

B. The sample must be large enough that the Central Limit Theorem applies.

C. The sample is randomly selected from the population. Your answer is correct.

D. The sample has a relative frequency distribution that is approximately normal.

Answer 1

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