Question

In: Statistics and Probability

A random sample of the ACT scores of 300 students at Big State University provided a...

A random sample of the ACT scores of 300 students at Big State University provided a sample mean score of 21.8 with a sample standard deviation of 5.632. Find the 95% confidence interval for the mean score of all Big State students who had taken the ACT.?
(a) (21.2, 22.4) (b) (21.0, 22.6) (c) (20.9, 22.7) (d) (20.3, 23.3) (e) (21.3, 22.3)

Solutions

Expert Solution

Solution :

Given that,

= 21.8

s = 5.632

n = 300

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Margin of error = E = Z/2* ( /n)

= 1.96 * ( 5.632/ 300)

= 0.64

At 95% confidence interval estimate of the population mean is,

- E < < + E

21.8 - 0.64 < < 21.8 = 0.64

21.2< < 22.4

(21.2,22.4 )

correct answer is (a)

orchestra answered 2 years ago
Next > < Previous

Related Solutions

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...
Out of a random sample of 355 freshman at State University, 192 students have declared a...
Out of a random sample of 355 freshman at State University, 192 students have declared a major. Find a 96% confidence interval for the true population proportion of freshman at State University who have declared a major. Find the left endpoint of the confidence interval . Round to three decimal places
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.
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 15.7 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.
The scores of a physics test of a random sample of students (n = 8) are...
The scores of a physics test of a random sample of students (n = 8) are listed below. Is the sample significantly different from m = 65? State the null and alternative hypotheses Set the criteria for a decision: two-tailed test with a = .05 Compute the test statistic using SPSS What is the effect size (you will need to compute Cohen’s d from data given in the SPSS output table) d= M- μ / (SD) (5 pts) Write the...
In a local university, 40% of the students live in the dormitories. A random sample of...
In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. The probability that the sample proportion (the proportion living in the dormitories) is at least 0.30 is Select one: a. 0.0336 b. 0.9664 c. 0.9328 d. 0.4664
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...
In a random sample of 100 college students, scores on a test were normally distributed with...
In a random sample of 100 college students, scores on a test were normally distributed with a mean of 80 points and standard deviation of 12 points. Use this scenario to answer the following questions: A. In this scenario, what is the point estimate? [2 points] B. Construct a 95% confidence interval to estimate the mean score in the population of all college students. Remember to show all work. Round your final answer to 3 decimal places. [4 points] C....
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...
A random sample of 28 students at a particular university had a mean age of 22.4...
A random sample of 28 students at a particular university had a mean age of 22.4 years. If the standard deviation of ages for all university students is known to be 3.1 years ,Find a 90% confidence interval for the mean of all students at that university.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT