For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the National Council intends to estimate the proportion from a random sample. Let p be the proportion of small businesses that declared Chapter 11 bankruptcy last year. (a) If no preliminary sample is taken to estimate p, how large a sample is necessary to be 99% sure that a point estimate p̂ will be within a distance of 0.08 from p? (Round your answer up to the nearest whole number.) ?? small businesses (b) In a preliminary random sample of 30 small businesses, it was found that eleven had declared Chapter 11 bankruptcy. How many more small businesses should be included in the sample to be 99% sure that a point estimate p̂ will be within a dista
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.
The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the National Council intends to estimate the proportion from a random sample. Let p be the proportion of small businesses that declared Chapter 11 bankruptcy last year.
?? small businesses
(b) In a preliminary random sample of 30 small businesses, it was found that eleven had declared Chapter 11 bankruptcy. How many more small businesses should be included in the sample to be 99% sure that a point estimate p̂ will be within a distance of 0.080 from p? (Round your answer up to the nearest whole number.)
?? more small businesses
Given Information :
The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the National Council intends to estimate the proportion from a random sample.
Let p be the proportion of small businesses that declared Chapter 11 bankruptcy last year.
(a)
At 99% confidence level , = 1 - 0.98 = 0.02 .
Critical value of z : zc = z(1-)/2 = z0.01 .
Using standard normal table z0.01 = 2.32
Provided margin of error = 0.08 . It's formula is given as :
For no preliminary , take standard proportion p = 0.05 .
Therefore , sample size n computed as :
=
n = 210.25
Largest sample size : n = 211 small businesses
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