Question

Use the information below for the following 3 questions A recent survey of 80 IU students and 60 Ball State students found that the percent of IU students who are part of Greek life is 18%, while the percent Ball State students who are part of Greek life is 15%. Find the 95% confidence interval for the difference between the proportion of IU students who are part of Greek life compared to Ball State students, i.e. LaTeX: D=p_{IU}-p_{Ball\:State} D = p I U − p B a l l S t a t e . [.0222 ; .0378] [-.0740 ; .1340] [-.1340 ; .0740] [-.0935 ; .1535] Flag this Question Question 13 1 pts Suppose you want to test for whether Greek participation is greater at IU than at Ball State. Which of the following would be the hypothesis test? LaTeX: \left(D=p_{IU}-p_{Ball\:State}\right) ( D = p I U − p B a l l S t a t e ) LaTeX: H_0 \colon D\ge0 ; H_A \colon D<0 H 0 : D ≥ 0 ; H A : D < 0 H 0 : D ≥ 0 ; H A : D < 0 LaTeX: H_0 \colon D=0 ; H_A \colon D\ne0 H 0 : D = 0 ; H A : D ≠ 0 H 0 : D = 0 ; H A : D ≠ 0 LaTeX: H_0 \colon D\ne0 ; H_A \colon D=0 H 0 : D ≠ 0 ; H A : D = 0 H 0 : D ≠ 0 ; H A : D = 0 LaTeX: H_0 \colon D\le0 ; H_A \colon D>0 H 0 : D ≤ 0 ; H A : D > 0 H 0 : D ≤ 0 ; H A : D > 0 Flag this Question Question 14 1 pts What is the test statistic for the difference between IU and Ball State Greek life participation, using the sample proportions found above? Recall:LaTeX: D=p_{IU}-p_{Ball\:State} D = p I U − p B a l l S t a t e (Round intermediate calculations to the third decimal) 0.471 -7.394 1.348 2.209

Answer 1

Solution

Let p₁ and p₂ represent the population proportion of IU students who are part of Greek life and Ball State students respectively.

Q1 : Confidence Interval

100(1 - α) % Confidence Interval for (p₁ - p₂) is:

[(p_1hat – p_2hat) ± MoE, …………………………………………………….. (1)

where

MoE = (Z_α/2)√[p_hat(1 – p_hat){(1/n₁) + (1/n₂)}] ……………………………….. (2)

with

p_1hat = (x/n₁),

p_2hat = (y/n₂),

p_hat = (n₁ p_1hat + n₂ p_2hat)/( n₁ + n₂),

Z_α/2 is the upper (α /2)% point of N(0, 1),

n₁ and n₂ being the two sample sizes.

So, 95% confidence interval for the difference between the proportion of IU students who are part of Greek life compared to Ball State students is: [- 0.0949, 0.1549) Fourth Option Answer 1

Details of calculations

n1	80
n2	60
x	14.4
y	9
p1hat	0.18
p2hat	0.15
phat	0.16714286
α	0.05
Zα/2	1.95996398
MoE	0.12488798
LB	-0.094888
UB	0.154888

Q2 : Test Hypotheses

Hypotheses:

Null H₀ : p₁ = p₂   Vs H_A : p₁ > p₂Answer 2

Q3 Test Statistic

Z = (p_1hat – p_2hat)/√[p_hat(1 - p_hat){(1/n₁) + (1/n₂)} = 0.471 First Option Answer 3

where p_1hat and p_2hat are sample proportions,

n₁, n₂ are sample sizes and

p_hat = {(n₁ x p_1hat) + (n₂ x p_2hat)}/(n₁ + n₂).

Details of calculations

n1	80
n2	60
x	14.4
y	9
p1hat	0.18
p2hat	0.15
phat	0.167142857
Zcal =	0.470813262

DONE