p ¯ 1 = 0.86, n 1 = 392, p ¯ 2 = 0.97, n 2...

p ¯ 1 = 0.86, n 1 = 392, p ¯ 2 = 0.97, n 2 = 289.Construct the 90% confidence interval for the difference between the population proportions.

Expert Solution

The pooled sample proportion(P) = ( * n1 + * n2)/(n1 + n2)

= (0.86 * 392 + 0.97 * 289)/(392 + 289)

= 0.9067

At 90% confidence level, the critical value is z_0.05 = 1.645

The 90% confidence interval is

() +/- z_0.05 * sqrt(P(1 - P)(1/n1 + 1/n2))

= (0.86 - 0.97) +/- 1.645 * sqrt(0.9067 * (1 - 0.9067) * (1/392 + 1/289))

= -0.11 +/- 0.0371

= -0.1471, -0.0729

orchestra answered 2 years ago

Prove via induction the following properties of Pascal’s Triangle: •P(n,2)=(n(n-1))/2 • P(n+m+1,n) = P(n+m,n)+P(n+m−1,n−1)+P(n+m−2,n−2)+···+P(m,0) for all...

Prove via induction the following properties of Pascal’s Triangle: •P(n,2)=(n(n-1))/2 • P(n+m+1,n) = P(n+m,n)+P(n+m−1,n−1)+P(n+m−2,n−2)+···+P(m,0) for all m ≥ 0

11.A population has a proportion equal to 0.86. Calculate P(p̄< 0.8) with n = 100.

Prove that for all integers n ≥ 2, the number p(n) − p(n − 1) is...

Prove that for all integers n ≥ 2, the number p(n) − p(n − 1) is equal to the number of partitions of n in which the two largest parts are equal.

For each positive integer, n, let P({n}) =(1/2^n) . Consider the events A = {n :...

For each positive integer, n, let P({n}) =(1/2^n) . Consider the events A = {n : 1 ≤ n ≤ 10}, B = {n : 1 ≤ n ≤ 20}, and C = {n : 11 ≤ n ≤ 20}. Find (a) P(A), (b) P(B), (c) P(A ∪ B), (d) P(A ∩ B), (e) P(C), and (f) P(B′). Hint: Use the formula for the sum of a geometric series

A Mystery Algorithm Input: An integer n ≥ 1 Output: ?? Find P such that 2^p...

A Mystery Algorithm Input: An integer n ≥ 1 Output: ?? Find P such that 2^p is the largest power of two less than or equal to n. Create a 1-dimensional table with P +1 columns. The leftmost entry is the Pth column and the rightmost entry is the 0th column. Repeat until P < 0 If 2^p≤n then put 1 into column P set n := n - 2^p Else put 0 into column P End if Subtract 1...

A wheel with a weight of 392 N comes off a moving truck and rolls without...

A wheel with a weight of 392 N comes off a moving truck and rolls without slipping along a highway. At the bottom of the hill it is rotating at an angular velocity of 27.7 rad/s. the radius of the wheel is .596 m and its moment of inertia about its rotation axis is .800 MR^2. Friction does work on the wheel as it rolls up the hill to a stop at a height of h about the bottom of...

Given n ∈N and p prime number and consider the polynomial f (x) = xn (xn-2)+1-p...

Given n ∈N and p prime number and consider the polynomial f (x) = xn (xn-2)+1-p 1)Prove that f (x) is irreducible in Q [x] 2) If n = 1 and p = 3, find Q [x] / f (x)) 3) Show that indeed Q [x] / (f (x)) is a field in the previous paragraph PLEASE answer all subsections

Considerapopulationwhoseprobabilitiesaregivenby p(1)=p(2)=p(3)= 1 3 (a) DetermineE[X]. (b) DetermineSD(X). σ2σ n =√n SD(X)= In the preceding formula,...

Considerapopulationwhoseprobabilitiesaregivenby p(1)=p(2)=p(3)= 1 3 (a) DetermineE[X]. (b) DetermineSD(X). σ2σ n =√n SD(X)= In the preceding formula, σ is the population standard deviation, and n is the (c) Let X denote the sample mean of a sample of size 2 from this population. Determine the possible values of X along with their probabilities. (d) Usetheresultofpart(c)tocomputeE[X]andSD(X). (e) Areyouranswersconsistent?

Find the values of p for which the series is convergent (a) Σ(n=2 to ∞) 1/n(ln...

Find the values of p for which the series is convergent (a) Σ(n=2 to ∞) 1/n(ln n)^p (b) Σ(n=2 to ∞) n(1+n^2)^p HINT: Use the integral test to investigate both

n = 5 p or π = 0.15 P(X<2) =

Question