Quiz 5 Hypothesis Test z-test y percent of the items produced hy a machine are d

Question

Quiz 5 Hypothesis Test z-test y percent of the items produced hy a machine are defective. A random sample of 81 items is selectel and checked for defects. 20 points a. What is the expected value of the sampling distribution of p? b. What is the standard deviation of the sampling dstnbution of p? c h shf p d. What is the random variable in this problem? Define t in words e. What is the probability thst the proportion af defective toms produced by the machine in the sample is between 0.15 and 0.277 what is the probablity that more than 30 5% of items produced by the machine in the sample is defective? f. g. What is the probøbility that the proportcn of delectve hems produced by the machine in the sample is at most 0.10? what is the maximum proportion for the bottom 10% or deletivo nema proced the machine in the sample? h.

Explanation / Answer

a)

sample proportion p=0.20

b) std deviation of sampling distribution of p=(p*(1-p)/n)1/2 =0.0444

c) as n=81 and p=0.2 therefore np >=10 and n(1-p)>=10

hence the shape will be approximately normal

d)

random variable is sample proportion of defective in 81 items

e)

f)

g)

h)

for 10th precentile ; z =-1.2816

hence corresponding percentile =mean +z*std error =0.2-1.2816*0.0444 =0.1430

for normal distribution z score =(phat-p)/p

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