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pr47723
04.06.2020 •
Mathematics
Many individuals over the age of 40 develop intolerance for milk and milk-based products. A
dairy has developed a line of lactose-free products that are more tolerable to such individuals. To
assess the potential market for these products, the dairy commissioned a market research study of individuals over 40 years old in its sales area. A random sample of 250 individuals showed that 86 of them suffer from milk intolerance. Based on the sample results, calculate a 90% confidence
interval for the population proportion that suffers milk intolerance. Interpret this confidence interval.
a) First, show that it is okay to use the 1-proportion z-interval. (Assumptions)
b) calcuate by hand a 90% confidence interval (use the formula)
c) provide an interpretation (conclusion)
d) if the level of confidence was 95% instead of 90% would the resulting interval be narrower or wider? explain. (show your computation before your explanation)
e) if the researchers were interested in the 90% interval with the 3% margin of error what size sample would they require?
f) verify your 90% confidence interval using your calculator.
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Ответ:
p = 86/250 = 0.344
z_c = 1.65 at 90% confidence.
margin of error, E = sqrt(pq/n)*z_c
= sqrt(0.344*(1-0.344)/250)*1.65
= 0.0496
90% CI = (p -E , p + E)
= (0.344 - 0.0496 , 0.344 + 0.0496)
= (0.2944, 0.3936) (Ans.)
Step-by-step explanation:
Ответ:
Answer is in the photo. I can't attach it here, but I've uploaded it to a file hosting. link below! Good Luck!
cutt.ly/Kzv78uJ