Identify the distribution (normal, Student t, chi-square) that should be used in each of the fo llowing situations. If none of the three distributions can be used, what other method could be used? In constructing a confidence interval estimate of p, you have 1200 survey respondents and 5% of them answered "yes" to the first question.

dizxindlert7

dizxindlert7

Answered question

2022-09-12

Identify the distribution (normal, Student t, chi-square) that should be used in each of the fo llowing situations. If none of the three distributions can be used, what other method could be used? In constructing a confidence interval estimate of p, you have 1200 survey respondents and 5% of them answered "yes" to the first question.

Answer & Explanation

London Maldonado

London Maldonado

Beginner2022-09-13Added 13 answers

IN GENERAL
Normal distribution: confidence interval for the mean μ with σ known (sampling distribution of the sample mean should be approximately normal)
Normal distribution: confidence interval the proportion p (number of successes and number of failures should both be at least 5).
Student t distribution: confidence interval for the mean μ with σ unknown (sampling distribution of the sample mean should be approximately normal)
Chi-square distribution: confidence interval for the standard deviation σ or the variance σ 2 (population distribution should be normal)
If none of the three distributions can be used, then we can use the bootstrap method.
Answer:
n=1200
p=5%=0.05
We should use the normal distribution, because we are interested in a confidence interval for the population proportion p.
The requirement of at least 5 successes and at least 5 failures is also satisfied, because there are np=1200(0.05)=60 successes and n(1-p)=1200(1-0.05)=1140 failures.
Result:
Normal distribution

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?