QUESTION 1:

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 541 judges, it was found that 292 were introverts.

(a)

Let p represent the proportion of all judges who are introverts. Find a point estimate for p.

(b)

Find a 99% confidence interval for p.

Give a brief interpretation of the meaning of the confidence interval you have found. SHOW ME EVERY STEP!

(c)Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration.

QUESTION 2:

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a marketing survey, a random sample of 741 women shoppers revealed that 623 remained loyal to their favorite supermarket during the past year (i.e., did not switch stores).

(a)

Let p represent the proportion of all women shoppers who remain loyal to their favorite supermarket. Find a point estimate for p.

(b)

Find a 95% confidence interval for p.

Give a brief explanation of the meaning of the interval. SHOW ME EVERY STEP!

(c)As a news writer, how would you report the survey results regarding the percentage of women supermarket shoppers who remained loyal to their favorite supermarket during the past year?

What is the margin of error based on a 95% confidence interval?