A random sample of size nequals400 yielded ModifyingAbove p with caretequals0.35. a. Is the sample size large enough to use the large sample approximation to construct a confidence interval for p? Explain. b. Construct a 90% confidence interval for p. c. Interpret the 90% confidence interval. d. Explain what is meant by the phrase "90% confidence interval."

a) i) np = 400*0.35=140 >10

ii) n(1-p)=400*(1-0.35) = 260>10

So then we can use the large sample approximation for this case

b)  

c) For this case we can conclude with a 90% of confidence that the true proportion of interest is between 0.311 and 0.389

d) For this case the 90% represent the confidence level for the proportion interval

Step-by-step explanation:

Part a

We can check the assumption with these two rules:

i) np = 400*0.35=140 >10

ii) n(1-p)=400*(1-0.35) = 260>10

So then we can use the large sample approximation for this case

Part b

The confidence interval would be given by this formula  

For the 90% confidence interval the value of and , and the critical value would be  

Replacing we got:

Part c

For this case we can conclude with a 90% of confidence that the true proportion of interest is between 0.311 and 0.389

Part d

For this case the 90% represent the confidence level for the proportion interval

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tony b

mar 21, 2017

answer:

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