Refer to the following for Questions 36-40. According to a survey, only 15% of c

Question

Refer to the following for Questions 36-40. According to a survey, only 15% of customers who visited the website of a major retail store made a purchase. Random sample sizes of 50 are selected. 36. The standard error of all the sample proportions of customers who will make a purchase after visiting the website is a) 0.0547 b) 0.0030 c) 0.0505 d) 0.1500 37, what proportion of the samples will have between 20% and 30% of customers who will make a purchase after visiting the website? a) 0.9900 b) 0.1596 c) 0.8389 d) 0.9985 38. What proportion of the samples will have less than 15% of customers who will make a purchase after visiting the website? a) 0.50 b) 0.30 c) 0.15 d) 0.25 39.90% of the samples will have less than what percentage of customers who will make a purchase after visiting the website? a) 8.54% b)50% c) 15% d) 21.47% 40.90% of the samples will have more than what percentage of customers who will make a purchase after visiting the website? a) 21.47% b) 23.5% c) 8.54% d) 15%

Explanation / Answer

36)

p=0.15

n=50

std error =(p*(1-p)/n)1/2 =0.0505 ; option C is correct

37)

as z score=(phat-p)/std error

P(0.2<P<0.3)=P(0.99<Z<2.97)=0.9985-0.8389 =0.1596

option B

38)

P(X<0.15)=P(Z<0)=0.5

option A

39)

for 90th percentile ; z=1.28

hence correponding value =estimated proportion +z*std error=0.15+1.28*0.0505=21.47%

40)

for 10th percentile ; z=-1.28

hence correponding value =estimated proportion +z*std error=0.15-1.28*0.0505=8.54%

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