Question

Strategic placement of lobster traps is one of the keys for a successful lobster fisherman. A study was conducted of the average distance separating traps, called trap spacing, deployed by lobster fishermen. The trap-spacing measurements (in meters) for a sample of seven teams from fishing cooperative A, and a sample of eight teams from fishing cooperative B are repeated in the accompanying table. For this problem, we are interested in comparing the mean trap-spacing measurements of the two fishing cooperatives. (Since the sample from fishing cooperative A is listed first, treat it as the first sample.) A Cooperative: 102 83 86 89 99 103 70 B Cooperative: 67 130 141 106 144 78 79 89 a. Compute a point estimate of the target parameter. b. Find a 95% confidence interval for the target parameter.

          Strategic placement of lobster traps is one of the keys for a successful lobster fisherman. A study was conducted of the average distance separating traps, called trap spacing, deployed by lobster fishermen. The trap-spacing measurements (in meters) for a sample of seven teams from fishing cooperative A, and a sample of eight teams from fishing cooperative B are repeated in the accompanying table. For this problem, we are interested in comparing the mean trap-spacing measurements of the two fishing cooperatives. (Since the sample from fishing cooperative A is listed first, treat it as the first sample.)

A Cooperative: 102
83
86
89
99
103
70

B Cooperative: 67
130
141
106
144
78
79
89

a. Compute a point estimate of the target parameter.
b. Find a 95% confidence interval for the target parameter.

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Added by Melissa A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Sheryl Ezze

11/30/2022

Step 1

For cooperative A, the mean is (102+83+86+89+99+103+70)/7 = 90.57 meters. For cooperative B, the mean is (67+130+141+106+144+78+79+89)/8 = 104.25 meters. a. The point estimate of the target parameter, which is the difference between the two means, is 104.25 - Show more…

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Strategic placement of lobster traps is one of the keys for a successful lobster fisherman. A study was conducted of the average distance separating traps, called trap spacing, deployed by lobster fishermen. The trap-spacing measurements (in meters) for a sample of seven teams from fishing cooperative A, and a sample of eight teams from fishing cooperative B are repeated in the accompanying table. For this problem, we are interested in comparing the mean trap-spacing measurements of the two fishing cooperatives. (Since the sample from fishing cooperative A is listed first, treat it as the first sample.) A Cooperative: 102 83 86 89 99 103 70 B Cooperative: 67 130 141 106 144 78 79 89 a. Compute a point estimate of the target parameter. b. Find a 95% confidence interval for the target parameter.

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Transcript

00:01 You have two samples and you have two cooperatives.

00:03 You have cooperative a and cooperative b.

00:06 And the sample size here was seven.

00:09 Sample size here was eight.

00:11 And the mean of those values from a is 90 .286, i'll say.

00:21 And for b, that mean is 104 .25.

00:26 The sample standard deviation for a is 11 .968 and that for b is 30 .574.

00:40 And again, the sample sizes are i gave up here.

00:45 And you want to find in part a, you're interested in finding an estimate for the difference between the mean of a and b.

00:57 We're going to use this sample first.

00:59 So your point estimate is to use the x bar of a, which is that 90 .286 minus the 104 .25.

01:12 And so when we take that 104 .25 and subtract the, it's actually this minus that.

01:21 It will be a negative answer.

01:23 We know 90 .286 minus that 1004 .25.

01:27 We end up getting a point estimate.

01:29 Is negative 13 .964.

01:32 So that's what we estimate.

01:34 But again, we know there's variability and we get more samples of size 8 or size 7 or size 8 that we anticipate getting different results.

01:43 And so this won't always stay the same.

01:45 And we can see we have quite a bit of variability...

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