Question

1)In a sample of 300 trees on someone’s orchard, A proportion of 0.78 were peach trees.

Construct a 90% confidence interval for the total population proportion of peach trees

in the entire orchard

2) Suppose A is the lower bound of the confidence interval you calculated in the previous problem. If you instead calculated a 99% confidence interval, would your lower bound be less than A or greater than A?

Answer 1

1).given data are:-

sample size (n) = 300

sample proportion () = 0.78

z critical value for 90% confidence level, both tailed test be:-

the 90% confidence interval for the total population proportion of peach trees in the entire orchard is :-

b).If i calculate a 99% confidence interval,the lower bound will be less than A .

[ A is the lower limit of the 90% confidence interval.

if we construct a 99% confidence interval, then the lower limit will be less than A,i.e, less than 0.741.

As,we know that when confidence level increases the confidence interval become more wide., in order to be more confident..so, the margin of error will increase..which will cause a decrease in the lower limit and an increase in upper limit.]

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