Question

An institute reported that 63 % of its members indicate that lack of ethical culture within financial firms has contributed most to the lack of trust in the financial industry. Suppose that you select a sample of 100 institute members. Complete parts (a) through (d) below.

a. What is the probability that the sample percentage indicating that lack of ethical culture within financial firms has contributed the most to the lack of trust in the financial industry will be between 56 % and 67 %? _______

(Type an integer or decimal rounded to four decimal places as needed.)

b. The probability is 90% that the sample percentage will be contained within what symmetrical limits of the population percentage?

The probability is 90 % that the sample percentage will be contained above____ % and below_____ %. (Type integers or decimals rounded to one decimal place as needed.)

c. The probability is 97% that the sample percentage will be contained within what symmetrical limits of the population percentage?

The probability is 97 % that the sample percentage will be contained above____ % and below_____ %.

(Type integers or decimals rounded to one decimal place as needed.)

d. Suppose you selected a sample of 400 institute members. How does this change your answers in (a) through (c) ?

A. An increase in sample size increases the standard error, causing the value of the answer to part (a) to decrease and the ranges in parts (b) and (c) to widen.

B. An increase in sample size decreases the standard error, causing the value of the answer to part (a) to decrease and the ranges in parts (b) and (c) to narrow.

C. An increase in sample size increases the standard error, causing the value of the answer to part (a) to increase and the ranges in parts (b) and (c) to widen.

D. An increase in sample size decreases the standard error, causing the value of the answer to part (a) to increase and the ranges in parts (b) and (c) to narrow.

Answer 1

Solution:-

n = 100

a) The probability that the sample percentage indicating that lack of ethical culture within financial firms has contributed the most to the lack of trust in the financial industry will be between 56 % and 67 % is 0.722.

p₁ = 0.56

p₂ = 0.67

By applying normal distruibution:-

z₁ = - 1.45

z₂ = 0.829

P( -1.45 < z < 0.829) = P(z > - 1.45) - P(z > 0.829)

P( -1.45 < z < 0.829) = 0.926 - 0.204

P( -1.45 < z < 0.829) = 0.722

b) The probability is 90 % that the sample percentage will be contained above 55.1 % and below 70.94%.

C.I = 0.63 + 1.645 × 0.04828

C.I = 0.63 + 0.07942

C.I = (0.551, 0.7094)

c) The probability is 97 % that the sample percentage will be contained above 52.52 % and below 73.48 %.

C.I = 0.63 + 2.17 × 0.04828

C.I = 0.63 + 0.10477

C.I = (0.5252, 0.7348)

d) D. An increase in sample size decreases the standard error, causing the value of the answer to part (a) to increase and the ranges in parts (b) and (c) to narrow.