The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the brand. How many adults must he survey in order to be 95% confident that his estimate is within eight percentage points of the true population percentage? Complete parts (a) through (c) below.a) Assume that nothing is known about the percentage of adults who have heard of the brandb) Assume that a recent survey suggests that about 81% of adults have heard of the brand.c) Given that the required sample size is relatively small, cculd he simply survey the adults at the nearest college?

a. No, a sample of students at the nearest college is a cluster sample, not a simple random sample, so it is very possible that the results would not be representative of the population of adults.

b. Yes, a sample of students at the nearest college is a simple random sample, so the resuls should be representative of the population of adults.

c. No, a sample of students at the nearest college is a stratified sample, not a simple random sample, so it is very possible that the results would not be representaive of the population of adults.

d. No, a sample of students at the nearest college is a convenience sample, not a simple randmom sample. so it is very possible that the results would not be representative of the population of adults.

Given Information:

Confidence level = 95%

Estimated error = 8%

Required Information:

(a) sample size = n = ?

(b) sample size = n = ?

(c) could he simply survey the adults at the nearest college?

(a) sample size = n = 150

(b) sample size = n = 92

(c) d. No, a sample of students at the nearest college is a convenience sample, not a simple random sample. so it is very possible that the results would not be representative of the population of adults.

Step-by-step explanation:

(a) In this part we are required to assume that nothing is known about the percentage of adults who have heard about the brand.

Since we dont know about the percentage of adults who have heard about the brand, we will assume that it is 50%

The z value corresponding 95% confidence level is 1.96

n = z²*p*(1-p)/ο²

n = (1.96²*0.50(1-0.50))/0.08²

n = 150.06

n ≈ 150

So we need a bigger sample size in this case.

(a) In this part we are required to assume that 81% of adults have heard about the brand.

n = z²*p*(1-p)/ο²

n = (1.96²*0.81(1-0.81))/0.08²

n = 92.37

n ≈ 92

So we need a smaller sample size in this case.

(c) could he simply survey the adults at the nearest college?

No, because convenience samples are most likely to be biased therefore, we should avoid such methodology for sampling.

d. No, a sample of students at the nearest college is a convenience sample, not a simple random sample. so it is very possible that the results would not be representative of the population of adults

A

Step-by-step explanation:

cosB = = =

Rationalise the denominator by multiplying numerator/denominator by

= ( divide 6 and 15 by 3 )

=

Hence

cosB = → A