Question

can i get help answering these questions please i do not understand how to solve them im having trouble please.

Question Hop 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 90% confident that his estimate is within seven 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 brand, n (Round up to the nearest integer.) b) Assume that a recent survey suggests that about 79% of adults have heard of the brand, dhid (Round up to the nearest integer.) c) Given that the required sample size is relatively small, could he simply survey the adults at the nearest college? O A. Yes, a sample of students at the nearest college is a simple random sample, so the results should be representative of the population of adults. OB. 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 representative of the population of adults. OC. 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. OD. 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.

Answer 1

Ans a ) using excel>Addin>phstat> sample size

we have

Sample Size Determination
Data
Estimate of True Proportion	0.5
Sampling Error	0.07
Confidence Level	90%
Intermediate Calculations
Z Value	-1.6449
Calculated Sample Size	138.0379
Result
Sample Size Needed	138

a ) n = 138

Sample Size Determination
Data
Estimate of True Proportion	0.79
Sampling Error	0.07
Confidence Level	90%
Intermediate Calculations
Z Value	-1.6449
Calculated Sample Size	91.6020
Result
Sample Size Needed	92

b ) n = 92

c ) option c is true

Ans 2 ) using excel>Addin>phstat>confidence interval

we have

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	6.2
Sample Mean	33.7
Sample Size	192
Confidence Level	90%
Intermediate Calculations
Standard Error of the Mean	0.447446459
Degrees of Freedom	191
t Value	1.6529
Interval Half Width	0.7396
Confidence Interval
Interval Lower Limit	32.96
Interval Upper Limit	34.44

the confidence interval is

32.96 <u < 34.44

option b is true .

Ans 3 ) using excel>addin>phstat>sample size

we have

Sample Size Determination
Data
Population Standard Deviation	16
Sampling Error	3
Confidence Level	95%
Intemediate Calculations
Z Value	-1.9600
Calculated Sample Size	109.2682
Result
Sample Size Needed	109

a _ n= 109

Sample Size Determination
Data
Population Standard Deviation	11.3
Sampling Error	3
Confidence Level	95%
Intemediate Calculations
Z Value	-1.9600
Calculated Sample Size	54.5018
Result
Sample Size Needed	56

b ) n = 56

c ) the result from part a has a larger sample size than in part b .the result from part a is likely to be better becasue of large sample size