6. -/5 pointsBBBasicStat7 8.3.017 For this problem, carry at least four digits a

Question

6. -/5 pointsBBBasicStat7 8.3.017 For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 20 out of 809 fish died when caught and released using barbless hooks on fles or lures. All hooks were removed from the fish. (a) Let p represent the proportion of all pike and trout that die (i.e., p is the mortality rate) when caught and released using barbless hooks. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 99% confidence interval for p. (Round your answers to three decimal places.) lower limit upper limit Give a brief explanation of the meaning of the interval. O 1% of the confidence intervals created using this method would include the true catch-and-release mortality rate. 99% of the confidence intervals created using this method would include the true catch-and-release mortality rate. O 99% of all confidence intervals would include the true catch-and-release mortality rate. O 1% of all confidence intervals would include the true catch-and-release mortality rate. (c) Is the normal approximation to the binomial justified in this problem? Explain. Yes; np 5. Need Help? Readh Talk to Tutor http://www.webassign.net/web/Student Assignment-Responses/last?dep-16624266 8/25/2017

Explanation / Answer

Part a

We are given X = 20 and n = 809

Point estimate = X/n = 20/809 = 0.0247

Part b

We have to find 99% confidence interval for population proportion.

Confidence interval = p-hat -/+ Z*sqrt(p-hat*q-hat/n)

Where Z is critical value for 99% confidence level

We have

p-hat = 0.024721879

q-hat = 1 - 0.024721879 = 0.975278

Sample size = n = 809

Critical value = Z = 2.5758

Confidence interval = 0.024721879 -/+ 2.5758*sqrt(0.024721879*0.975278/809)

Lower limit = 0.024721879 - 2.5758*sqrt(0.024721879*0.975278/809)

Lower limit = 0.024721879 - 0.0141

Lower limit = 0.011

Upper limit = 0.024721879 + 2.5758*sqrt(0.024721879*0.975278/809)

Upper limit = 0.024721879 + 0.0141

Upper limit = 0.039

Confidence interval = (0.011, 0.039)

Explanation:

99% of all confidence intervals would include the true catch and release mortality rate.

Part c

We have n = 809 and p = 0.024721879

np = 809*0.024721879 = 20

nq = 809*0.975278 = 789

np > 5 and nq > 5

Answer:

Yes, np>5 and nq>5

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