Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 480 eggs in group I, of which a field count showed about 275 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 874 eggs in group II boxes, of which a field count showed about 272 hatched. Find a point estimate ˆp1 and ˆp2 for the proportion of eggs that hatch in group I nest boxes and group II nest boxes. Let p1 and p2 be the population proportion of hatched count in boxes I and II respectively. Find a 99% confidence interval for p1 − p2. (a) List the given information with appropriate symbols. (b) What is the probability distribution of ˆp1−pˆ2, difference between sample proportions? (c) Write the expression for the population mean of ˆp1 − pˆ2 distribution. Use proper symbols. (d) Find the population standard deviation of ˆp1 − pˆ2 distribution. Use proper mathematical symbols. (e) Find the margin of error of ˆp1 − pˆ2 distribution for 99% confidence level. Draw bell curve showing critical values and confidence level. (f) Compute 99% confidence interval for p1 − p2, the difference between population proportion of eggs hatched. (g) Visualize the confidence interval in a number line. (h) Interpret the confidence interval in the context of the question
Group I nesting boxes were well separated from each other and well hidden by available
brush. There were a total of 480 eggs in group I, of which a field count showed about
275 hatched. Group II nesting boxes were placed in highly visible locations and grouped
closely together. There were a total of 874 eggs in group II boxes, of which a field count
showed about 272 hatched. Find a point estimate ˆp1 and ˆp2 for the proportion of eggs
that hatch in group I nest boxes and group II nest boxes. Let p1 and p2 be the population
proportion of hatched count in boxes I and II respectively. Find a 99% confidence interval
for p1 − p2.
(a) List the given information with appropriate symbols.
(b) What is the probability distribution of ˆp1−pˆ2, difference between sample proportions?
(c) Write the expression for the population mean of ˆp1 − pˆ2 distribution. Use proper
symbols.
(d) Find the population standard deviation of ˆp1 − pˆ2 distribution. Use proper mathematical symbols.
(e) Find the margin of error of ˆp1 − pˆ2 distribution for 99% confidence level. Draw bell
curve showing critical values and confidence level.
(f) Compute 99% confidence interval for p1 − p2, the difference between population proportion of eggs hatched.
(g) Visualize the confidence interval in a number line.
(h) Interpret the confidence interval in the context of the question
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