6. Estimate the proportion of small company CEos whose salary is over $500,000.

Question

6. Estimate the proportion of small company CEos whose salary is over $500,000. (a) Does the data set meet the criteria to use the procedure that we learned in class? i. Is the sample SRS? subject of independence, population ii. Have we the criteria for a binomial distribution? (on the them.) the we are examining is small businesses. Let us assume there are at least 1,200 of iii. Are there at least 5 successes and 5 failures? is over s500,000. (b) Construct a 95% confidence interval estimate of the proportion for CEOs whose salary (c) Put your result from part (c) into English. (d) What is the margin of error?

Explanation / Answer

Answer:

a). proportion p=18/60 =0.30

i).no information available.

ii). Yes, met the criteria, np > 10 and n(1-p) > 10.

iii). Yes,

b).

Confidence Interval Estimate for the Proportion

Data

Sample Size

60

Number of Successes

18

Confidence Level

95%

Intermediate Calculations

Sample Proportion

0.3

Z Value

1.9600

Standard Error of the Proportion

0.0592

Interval Half Width

0.1160

Confidence Interval

Interval Lower Limit

0.1840

Interval Upper Limit

0.4160

95% CI= (0.184, 0.416)

c). we are 95% confident that true proportion of CEO whose salary is over $500,000.

d). margin of error = 0.116

Confidence Interval Estimate for the Proportion

Data

Sample Size

60

Number of Successes

18

Confidence Level

95%

Intermediate Calculations

Sample Proportion

0.3

Z Value

1.9600

Standard Error of the Proportion

0.0592

Interval Half Width

0.1160

Confidence Interval

Interval Lower Limit

0.1840

Interval Upper Limit

0.4160

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