Problem 2: Online Books (4 points) A consumer research center surveyed 427 rando

Question

Problem 2: Online Books (4 points) A consumer research center surveyed 427 randomly selected women and found that 29% of them purchase books online. a. What is the number of women in this sample who said that they purchase books online? b. Find a 95% confidence interval estimate of the percentage of all women who purchase books online. 150816 Math215-Statistical Concepts Franklin University Name: Can we safely conclude that less than 40% of all women purchase books online? why or why not? Can we safely conclude that at least 25% of all women purchase books online? why or why not? C. d. Problem 3: Find the Sample Size (4 points) A pizza shop owner wishes to find the 95% confidence interval of the true mean cost of a large plain pizza. How large should the sample be if she wishes to be accurate to within $0.15? A previous study showed that the standard deviation of the price was $0.26. a. b. A researcher wishes to be 95% confident that her estimate of the true proportion of individuals who travel overseas is within 4% of the true proportion. Find the sample necessary if, in a prior study, a sample of 200 people showed that 40 traveled overseas last year. If no estimate of the sample proportion is available, how large should the sample be?

Explanation / Answer

a)

the number of women is

0.29*427 = 123.83 = 124 approx

b)
we know that the confidence interval for proportion is given as

p +- z*sqrt((p*1-p)/n)

we know that for 95% the z is 1.96

so

0.29 +- 1.96*sqrt(0.29*(1-0.29)/427)

solving this we get the interval as

0.246 and 0.33

c)
as the CI is 24.6% and 33.3% , we can be 95% confident that the less than 40% of all women purchases books online

d)

yes , again as the lower limit of the CI is 25% approx , we are 95% confident in saying that the atleast 25% of all women purchases books online

please note that we can answer only 1 question at a time , as per the answering guidelines

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