Question

Two random samples are taken, one from among first-year students and the other from among fourth-year...

Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifying the student Honor Code. A summary of the sample sizes and number of each group answering yes'' are given below:

First-Years (Pop. 1):Fourth-Years (Pop. 2):n1=84,n2=89,x1=57x2=64First-Years (Pop. 1):n1=84,x1=57Fourth-Years (Pop. 2):n2=89,x2=64

Is there evidence, at an α=0.1, level of significance, to conclude that there is a difference in proportions between first-years and fourth-years? Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic=

Note: For the next part, your answer should use interval notation. An answer of the form (−∞,a)(−∞,a) is expressed (-infty, a), an answer of the form (b,∞)(b,∞) is expressed (b, infty), and an answer of the form (−∞,a)∪(b,∞)(−∞,a)∪(b,∞) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is

Homework Answers

Answer #1

(A)

H0: Null Hypothesis: p1 = p2 ( There is no difference in proportions between first-years and fourth-years)

HA: Alternative Hypothesis: p1 p2 ( There is a difference in proportions between first-years and fourth-years) (Claim)

n1 = 84

1 = 57/84 = 0.6786

n2 = 89

2 = 64/89 = 0.7191

Pooled Proportion is given by:

Test Statistic is given by:

So,

The value of the standardized test statistic= - 0.581

(B)

= 0.10

From Table, critical values of Z = 1.64

The rejection region for the standardized test statistic:

(-infty, - 1.64)U(1.64, infty).

(C)

By Technology:

The p-value is 0.5612

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Two random samples are taken, one from among first-year students and the other from among fourth-year...
Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifying the student Honor Code. A summary of the sample sizes and number of each group answering yes'' are given below: First-Years (Pop. 1):Fourth-Years (Pop. 2):n1=86,n2=83,x1=50x2=58First-Years (Pop. 1):n1=86,x1=50Fourth-Years (Pop. 2):n2=83,x2=58 Is there evidence, at an α=0.065α=0.065 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years?...
Two random samples are taken, one from among first-year students and the other from among fourth-year...
Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifying the student Honor Code. A summary of the sample sizes and number of each group answering yes'' are given below: First-Years (Pop. 1):Fourth-Years (Pop. 2):n1=93,n2=97,x1=62x2=56First-Years (Pop. 1):n1=93,x1=62Fourth-Years (Pop. 2):n2=97,x2=56 Is there evidence, at an ?=0.07?=0.07 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years?...
Two random samples are taken, one from among first-year students and the other from among fourth-year...
Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifying the student Honor Code. A summary of the sample sizes and number of each group answering yes'' are given below: First-Years (Pop. 1):Fourth-Years (Pop. 2):n1=82,n2=84,x1=47x2=47 Is there evidence, at an α=0.035 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years? Carry out an appropriate...
Two random samples are taken, one from among first-year students and the other from among fourth-year...
Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifying the student Honor Code. A summary of the sample sizes and number of each group answering yes'' are given below: First-Years (Pop. 1): n1=96, x1=49 Fourth-Years (Pop. 2):n2=88, x2=54 Is there evidence, at an α=0.04 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years?...
1) Independent random samples, each containing 90 observations, were selected from two populations. The samples from...
1) Independent random samples, each containing 90 observations, were selected from two populations. The samples from populations 1 and 2 produced 21 and 14 successes, respectively. Test H0:(p1?p2)=0 against Ha:(p1?p2)?0. Use ?=0.07. (a) The test statistic is (b) The P-value is (c) The final conclusion is A. We can reject the null hypothesis that (p1?p2)=0 and accept that (p1?p2)?0. B. There is not sufficient evidence to reject the null hypothesis that (p1?p2)=0. 2)Two random samples are taken, one from among...
Two random samples are taken, one from among UVA students and the other from among UNC...
Two random samples are taken, one from among UVA students and the other from among UNC students. Both groups are asked if academics are their top priority. A summary of the sample sizes and proportions of each group answering yes'' are given below: UVA (Pop. 1):UNC (Pop. 2):n1=88,n2=90,p̂ 1=0.839p̂ 2=0.593UVA (Pop. 1):n1=88,p^1=0.839UNC (Pop. 2):n2=90,p^2=0.593 Find a 97.9% confidence interval for the difference p1−p2p1−p2 of the population proportions. Confidence interval =
(1 point) Two random samples are taken, one from among UVA students and the other from...
(1 point) Two random samples are taken, one from among UVA students and the other from among UNC students. Both groups are asked if academics are their top priority. A summary of the sample sizes and proportions of each group answering yes'' are given below: UVA (Pop. 1):UNC (Pop. 2):n1=88,n2=90,p̂ 1=0.839p̂ 2=0.593UVA (Pop. 1):n1=88,p^1=0.839UNC (Pop. 2):n2=90,p^2=0.593 Find a 97.9% confidence interval for the difference p1−p2p1−p2 of the population proportions. Confidence interval =
(1 point) Two random samples are taken, one from among UVA students and the other from...
(1 point) Two random samples are taken, one from among UVA students and the other from among UNC students. Both groups are asked if academics are their top priority. A summary of the sample sizes and proportions of each group answering yes'' are given below: UVA (Pop. 1):UNC (Pop. 2):n1=97,n2=95,p^1=0.724p^2=0.628 Find a 96.6% confidence interval for the difference p1−p2 of the population proportions. Confidence interval =
Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and...
Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below: Population 1: 71, 67, 61, 62, 67, 70, 68 Population 2: 71, 68, 71, 78, 76, 73, 71, 68 Is there evidence, at an α=0.075, level of significance, to conclude that there those who exercise regularly have lower resting heart rates? (Assume that the population variances are equal.) Carry out an...
(1 point) Random samples of resting heart rates are taken from two groups. Population 1 exercises...
(1 point) Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below: Population 1: 72, 62, 64, 64, 65, 72, 68 Population 2: 72, 74, 69, 71, 69, 72, 68, 68 Is there evidence, at an α=0.065α=0.065 level of significance, to conclude that there those who exercise regularly have lower resting heart rates? (Assume that the population variances are equal.) Carry...