Question

In: Statistics and Probability

A university financial aid office polled a random sample of 746 male undergraduate students and 828...

A university financial aid office polled a random sample of 746 male undergraduate students and 828 female undergraduate students. Each of the students was asked whether or not they were employed during the previous summer. 501 of the male students and 502 of the female students said that they had worked during the previous summer. Give a 95% confidence interval for the difference between the proportions of male and female students who were employed during the summer.

Step 1 of 3 : Find the point estimate that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 3: Construct the 90% confidence interval. Round your answers to three decimal places. Find the margin of error. Round your answer to six decimal places.

Step 3 of 3:Construct the 90%confidence interval. Round your answers to three decimal places.

Solutions

Expert Solution

Solution :

  For 95% confidence interval :

Step 1 :

     => Point estimate as p1 - p2 = 0.672 - 0.606 = 0.066

step 2 :

=> for 95% confidence interval, Z = 1.96

=> Margin of error E = Z*sqrt((p1*(1 - p1)/n1) + (p2*(1 - p2)/n2))

= 1.96*sqrt((0.672(1 - 0.672)/746) + (0.606*(1 - 0.606)/828))

= 0.047358

Step 3 :

=> The 95% confidence interval is

=> (p1 - p2) +/- E

=> 0.066 +/- 0.047358

=> (0.018642 , 0.113358)

=> (0.019 , 0.113) (rounded)

For 90% confidence interval :

Step 1 :

=> Point estimate as p1 - p2 = 0.672 - 0.606 = 0.066

step 2 :

=> for 90% confidence interval, Z = 1.645

=> Margin of error E = Z*sqrt((p1*(1 - p1)/n1) + (p2*(1 - p2)/n2))

= 1.645*sqrt((0.672(1 - 0.672)/746) + (0.606*(1 - 0.606)/828))

= 0.039747

Step 3 :

=> The 90% confidence interval is

=> (p1 - p2) +/- E

=> 0.066 +/- 0.039747

=> (0.026253 , 0.105747)

=> (0.026 , 0.106) (rounded)


  


Related Solutions

A university financial aid office polled a random sample of 839 male undergraduate students and 727...
A university financial aid office polled a random sample of 839 male undergraduate students and 727 female undergraduate students. Each of the students was asked whether or not they were employed during the previous summer. 505 of the male students and 563 of the female students said that they had worked during the previous summer. Give a 90% confidence interval for the difference between the proportions of male and female students who were employed during the summer. Step 1 of...
A university financial aid office polled a random sample of 528 male undergraduate students and 419...
A university financial aid office polled a random sample of 528 male undergraduate students and 419 female undergraduate students. Each of the students was asked whether or not they were employed during the previous summer. 404 of the male students and 248 of the female students said that they had worked during the previous summer. Give a 80% confidence interval for the difference between the proportions of male and female students who were employed during the summer. Step 1 of...
A university financial aid office polled a random sample of 801801 male undergraduate students and 858858...
A university financial aid office polled a random sample of 801801 male undergraduate students and 858858 female undergraduate students. Each of the students was asked whether or not they were employed during the previous summer. 571571 of the male students and 513513 of the female students said that they had worked during the previous summer. Give a 98%98% confidence interval for the difference between the proportions of male and female students who were employed during the summer. Step 2 of...
A university financial aid office polled a random sample of 528 528 male undergraduate students and...
A university financial aid office polled a random sample of 528 528 male undergraduate students and 651 651 female undergraduate students. Each of the students was asked whether or not they were employed during the previous summer. 295 295 of the male students and 463 463 of the female students said that they had worked during the previous summer. Give a 80% 80% confidence interval for the difference between the proportions of male and female students who were employed during...
A university financial aid office polled an SRS of undergraduate students to study their summer employment....
A university financial aid office polled an SRS of undergraduate students to study their summer employment. Not all students were employed in the previous summer. Among 797 students, 518 of them were employed. a. Is there evidence to support that the proportion of students employed during the summer is greater than 60%? Using a significance level 0.05. b. Construct a 95% confidence interval for the proportion of students who were employed during the summer.
In a large university, 20% of the students are male. If a random sample of twenty...
In a large university, 20% of the students are male. If a random sample of twenty two students is selected a. What is the probability that the sample contains exactly twelve male students? b. What is the probability that the sample will contain no male students? c. What is the probability that the sample will contain exactly twenty female students? d. What is the probability that the sample will contain more than nine male students? e. What is the probability...
You plan to take a random sample of 1000 undergraduate students enrolled at the University of...
You plan to take a random sample of 1000 undergraduate students enrolled at the University of Rochester to compare the proportion of female and male students who would like to see that the United States of America have a female President. b.Suppose that you use random numbers to select students, but you stop selecting females as soon as you have 100, and you stop selecting males once you have 100. Is the resulting sample a simple random sample? Why or...
I want to provide this solution for other students to see. A university financial aid office...
I want to provide this solution for other students to see. A university financial aid office polled a random sample of 591 male undergraduate students and 484 female undergraduate students. Each of the students was asked whether or not they were employed during the previous summer. 424424 of the male students and 385 of the female students said that they had worked during the previous summer. Give a 95% confidence interval for the difference between the proportions of male and...
A sample of 300 students of undergraduate and 300 students of postgraduate classes of a university...
A sample of 300 students of undergraduate and 300 students of postgraduate classes of a university were asked to give their opinion towards autonomous colleges. 190 of the undergraduate and 210 of the postgraduate students favoured the autonomous status. i) At 5% significance level, would it be said that the opinions of the undergraduate and postgraduate students on autonomous colleges are independent? {The critical value of the requisite test statistic is 3.84} ( ii) What is the implication / interpretation...
A random sample of 250 students at a university finds that these students take a mean...
A random sample of 250 students at a university finds that these students take a mean of 14.3 credit hours per quarter with a standard deviation of 1.5 credit hours. Estimate the mean credit hours taken by a student each quarter using a 98​% confidence interval.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT