Question

13. The National Institutes of Health funded a study of a random sample of 856 people age 71 and older in the United States. They found that 9.7% of these people suffer from Alzheimer’s Disease.

a.Is .097 (the decimal version of 9.7%) a parameter or a statistic? What symbol do you use to represent 0.097?

b.

First, calculate the lower end of the confidence interval.

Report your answer to three decimals and round appropriately; e.g., 0.xxx (3 points)

c.

Next, calculate the upper end of the interval.

Report your answer to three decimals and round appropriately; e.g., 0.xxx. (1 point)

d. If you were to calculate a 90% confidence interval, would it be wider or narrower than the 95% confidence interval? (1 point)

Answer 1

Answer)

A)

Parameter means entire population

Statistics means sample

As here we are considering a sample

So, it is a statistics

And we use the symbol p hat.

B)

First we need to check the conditions of normality that is if, n*p and n*(1-p) both are greater than 5 or not

N*p = 856*0.097 = 83

N*(1-p) = 773

As both are greater than 5, so conditions are met

And therefore, we can use standard normal z table to estimate the interval

Margin of error (MOE) = Z*√P*(1-P)/√N

From z table, critical value z for 95% confidence level is 1.96

And p = 0.097

N = 856

MOE = 0.0198266313396

Lower end = P-MOE = 0.0771733686603 = 0.077

C)

Upper end = P+MOE = 0.1168266313396

D)

As we can see that, width of the interval is directly proportional to the confidence level

As margin of error = z*√p*(1-p)/√n

That is as the confidence level increases margin of error also increases and hence the interval becomes wider

So, 90% is narrower than 95%.