I want to know how to get the answer and explain step by step please!
in Statistics Answers by
reshown

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

This looks like a binomial distribution where mean=np and variance=np(1-p). In this question p=sample proportion p hat.

So, with mean=500×0.9=450,  variance=500×0.9×0.1=45, standard deviation=√45=6.708 approx.

The standard error is standard deviation/n=6.708/500=0.0134 approx (I think!).

Now we need a t test critical value for 95% confidence level. The large sample size means we can use 1.96 as the critical value, which we get from t tables or normal distribution (z) tables for a significance level of 0.05.

We apply this critical value to the standard error to get the margin of error for the required confidence interval=1.96×0.0134=0.026 approx.

The test statistic is p=0.90, and the 95% confidence level means that we can apply a range of values for p: 0.90±0.026.

Therefore 0.900-0.026<p<0.900+0.026, that is, 0.874<p<0.926.

by Top Rated User (646k points)

Related questions

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
82,946 questions
87,612 answers
1,966 comments
4,298 users