## A random sample of 5120 permanent dwellings on an entire reservation showed that 1627 were traditional hogans. (a) Let p be the

Question

A random sample of 5120 permanent dwellings on an entire reservation showed that 1627 were traditional hogans.

(a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.)lower limit- ______________upper limit- ______________

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2021-10-10T22:49:45+00:00
2021-10-10T22:49:45+00:00 1 Answer
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## Answers ( )

Answer:a)

b)The 99% confidence interval would be given by (0.301;0.355)

Step-by-step explanation:1) Notation and definitions

number of permanent dwellings on the entire reservation that are traditional hogans.

random sample taken

estimated proportion of permanent dwellings on the entire reservation that are traditional hogans.

true population proportion of permanent dwellings on the entire reservation that are traditional hogans.

A

confidence intervalis “a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval”.The

margin of erroris the range of values below and above the sample statistic in a confidence interval.Normal distribution, is a “probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean”.The population proportion have the following distribution

Part aThe point of estimate for p=the proportion of all permanent dwellings on the entire reservation that are traditional hogans is given by:

Part bIn order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by and . And the critical value would be given by:

The confidence interval for the mean is given by the following formula:

If we replace the values obtained we got:

The 99% confidence interval would be given by (0.301;0.355)