Question

4. Sample Size What is the minimal sample size needed for a 99% confidence interval to have a maximal margin of error of 0.06:

1. if a preliminary estimate for p is 0.8?
2. if there is no preliminary estimate for p?

5. Myers-Briggs: Actors Isabel Briggs Myers was a pioneer in the study of personality types. The following information is taken from MBTI Manual: A Guide to the Development and Use of the Myers-Briggs Type Indicator by Myers and McCaulley (Consulting Psychologists Press). In a random sample of 62 professional actors, it was found that 39 were extroverts.

1. Let p represent the proportion of all actors who are extroverts. Find a point estimate for p.
2. Find a 95% confidence interval for p. Give a brief interpretation of the meaning of the confidence interval you have found.
3. Check Requirements Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration.

Answer 1

Answer:

4.

Given,

Margin of error E = 0.06

alpha = 1 - 0.99

= 0.01

Here for the 99% confidence interval , z critical value is 2.576

a)

To give the preliminary estimate for proportion p = 0.8

Now consider,

n = p(1-p)*(z/E)^2

substitute values

= 0.8(1 - 0.8)*(2.576/0.06)^2

= 0.16*1843.271111

= 294.9234

n = 295

b)

To give sample size if there is no preliminary estimate for p

let us consider,

p = 0.5 [unknown]

consider,

n = p(1-p)*(z/E)^2

substitute values

= 0.5(1 - 0.5)*(2.576/0.06)^2

= 460.82

n = 461

I hope it works for you.

Please post the remaining question as separate question. Thank you.