Problem 5 Forn the past experience the department store knows that 15% of itenns

Question

Problem 5 Forn the past experience the department store knows that 15% of itenns sold were returned. Based on a recently collected random sample of 100 sold items the following confidence interval was obtained for the population proportion of returned items (0.165,0.335) a) What is the sample proportion based on which this interval was con- structed? What is the margin of error of the interval in (1)? b) What is the confidence level of the interval in (1)? c) Based on the obtained confidence interval would you say that the percentage of returned items among sold items is now smaller, larger or equal to 15%?

Explanation / Answer

a) here sample proportion phat =(0.335+0.165)/2=0.25

margin of error =(0.335-0.165)/2=0.085

b) for above std error =(phat(!-phat)/n)1/2 =0.0433

hence for confidence interval critical z=margin of error/std error =~1.96

for above critical value of z ; confidence level is 95%

c)

here as confidence interval vales are larger then 15%(0.15) therefore % of returned items among sold items is now larger,

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