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2. Study of shark attacks on human show that 15th of 200 attacks occurred in deep water. Construct the 99% confidence interval for the true proportion of shark atta...

Question

2. Study of shark attacks on human show that 15th of 200 attacks occurred in deep water. Construct the 99% confidence interval for the true proportion of shark attacks that occur in deep water.a. given the sample data and problem 2 what is the best point estimate of the population proportion of shark attacks that occur and deep water?

2. Study of shark attacks on human show that 15th of 200 attacks occurred in deep water. Construct the 99% confidence interval for the true proportion of shark attacks that occur in deep water.a. given the sample data and problem 2 what is the best point estimate of the population proportion of shark attacks that occur and deep water?



Answers

Assume the sample is from a normally distributed population and construct the indicated confidence intervals for $(a)$ the population variance $\sigma^{2}$ and $(b)$ the population standard deviation $\sigma .$ Interpret the results. As part of a water quality survey, you test the water hardness in several randomly selected streams. The results are shown in the figure. Use a $95 \%$ level of confidence.

Produce problem. The sample is 200 fish cut in the lake, so let's write down and is 200 and ah, sample Mean is the mean length 13.3 Choose population standard deviation. 2.5 inches for part. A win in 90% confidence interval. So from the Debar McCarry members A is 1.645 or 65 for part B. Same question, but 90 a or set. So for four days and way with Cabaret, we don't know this by heart, but the numbers no for ah, the area the one the half Z is 1%. So point one 2.33 there for both of them. We need to calculate the end point you have That's right. Separately in the formula, the X bar we're subtract and we're hand the time sick. My almost croaked Offend. We have everything. So we have 14.3 plus and minus 1.65 times, 2.5 over 200. You know what? That the wrong will be 14 to be last minus two point B. That's 2.5. So we calculate will get the various for each one for far A. When we subtract begets 14.1 on the way to 14.59 and again as well increase the confidence. We should increase the interval. So if we calculate ah, the 98% confidence interval, there have different Z total number of standard. There's two point immediately and it's going to go from 13.89 or the way too 14.7 about you and that's the solution.

Problem. 23. The bar graph about UN provoking truck attacks. Eso would upward train in years 1990 to 2000 and five and the mean number off the shark attacks increased in the following years. But on the fatality rate decrease that also show an apparent condition, a contradiction since if shark attacks increases, then the fatality should also increase. But in the data's of Texas degrees, and doesn't this done that, Mexico?

So to find this confidence interval, we're going to take the proportion the 600 Out of 10,000, Which is again .6 minus The 720 out of 8000, That is the point oh nine. So that difference? So our differences from uh negative point oh three plus or minus the Z star value. And we're finding a 95% confidence interval. So that value is 1.96 and then times the square root of and this is our big standard deviation. We're going to take the .6 Times The compliment, which is .94 Over the 10,000 sample size Plus, we're going to take that .09 Times its complement which is .91 Over the sample size of 8000. And when we do that We end up taking this negative .03 and subtract away this quantity and the negative .03 plus that quantity. And it comes out to be negative .0378 up to negative 0.222 So we think that the P one minus P to that difference is somewhere between here mm and here.

So we know that first proportion is .18 And the second proportion is .16. And we want to find, so that's are different. So at .2 difference Plus remind us. And then we want the team of disease star value for 90 confidence, that's the 1.645. And then we find our big standard deviation. And for the confidence interval you do not use that waited pool, you use these actual values. So I take the .18 Times 2.82 Divided by the sample size which was 10,000. And I take the .16 Times its complement .84 divided by the sample size. That was 8000. And then we'll take this point oh two minus this quantity and the 20.2 plus that quantity. And when we do we get the interval comes out to be 0.10 But 10076, Our .01076 UP 2.0- 9- four. So we think that the difference between those actual proportions Is sandwich somewhere in here with 90 confidence


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