i know the answerse to all of these, the only problem is how to attain it?
1.Find the critical value zα/2 that corresponds to a 98% confidence level.
answer:2.33
2.Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
n = 125, x = 72; 90% confidence
3 Use the given data to find the minimum sample size required to estimate the population proportion.
Margin of error: 0.005; confidence level: 99%; from a prior study, p is estimated by 0.166.
1.Find the critical value zα/2 that corresponds to a 98% confidence level.
answer:2.33
2.Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
n = 125, x = 72; 90% confidence
3 Use the given data to find the minimum sample size required to estimate the population proportion.
Margin of error: 0.005; confidence level: 99%; from a prior study, p is estimated by 0.166.
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1. You can solve this problem two ways: with a calculator or using a z distribution table.
With a calculator:
1-.98=.02 This is your α-level, or the total area on your graph that is not covered by the 98% confidence level.
.02÷2=.01 Since it is a α/2, you need to divide the .02 between the two tails of the graph.
invNorm(.01)= -2.33 This is your zα/2 (Although the calculator will give you a negative answer, your answer is really ±2.33, since your critical values are placed symmetrically on both the negative and positive side of the graph.)
If you want to use the table, all you need to do is find the closest value to α/2 on the z-distribution table. For an area of .01, the closest value on the table is .0099, which corresponds to -2.33.
2. The formula for constructing a confidence interval for a proportion is:
p - (zα/2) √pq/n < P < p + (zα/2) √pq/n
p: sample proportion
q: 1-p
n: number of samples
P: population proportion
To find sample proportion, divide x by n. To find zα/2, use the same process as number 1. q is simply 1 minus p, and n is already given.
3. The formula for sample size is:
n = [(zα/2 * σ)÷E]^2
σ: standar deviation
E = maximum error of estimate
With a calculator:
1-.98=.02 This is your α-level, or the total area on your graph that is not covered by the 98% confidence level.
.02÷2=.01 Since it is a α/2, you need to divide the .02 between the two tails of the graph.
invNorm(.01)= -2.33 This is your zα/2 (Although the calculator will give you a negative answer, your answer is really ±2.33, since your critical values are placed symmetrically on both the negative and positive side of the graph.)
If you want to use the table, all you need to do is find the closest value to α/2 on the z-distribution table. For an area of .01, the closest value on the table is .0099, which corresponds to -2.33.
2. The formula for constructing a confidence interval for a proportion is:
p - (zα/2) √pq/n < P < p + (zα/2) √pq/n
p: sample proportion
q: 1-p
n: number of samples
P: population proportion
To find sample proportion, divide x by n. To find zα/2, use the same process as number 1. q is simply 1 minus p, and n is already given.
3. The formula for sample size is:
n = [(zα/2 * σ)÷E]^2
σ: standar deviation
E = maximum error of estimate
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Actually, I'm a girl, but you're very welcome anyway. Glad to help :)
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