Question

In: Statistics and Probability

Among those who take the Graduate Record Examination (GRE), 67 people are randomly selected. This sample...

Among those who take the Graduate Record Examination (GRE), 67 people are randomly selected. This sample group has a mean score of 558 and a standard deviation of 149 on the quantitative portion of the GRE. Find a 99% confidence interval estimate of the population mean.

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 558

Population standard deviation =    = 149
Sample size = n =67

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576   ( Using z table )

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

= 2.576 * ( 149/ 67)

= 46.8916

At 99% confidence interval estimate of the population mean is,

- E < < + E

558-46.8916 < < 558+46.8916

511.1084< < 604.8916

(511.1084, 604.8916)

orchestra answered 2 years ago
Next > < Previous

Related Solutions

The Graduate Record Examination (GRE) is a standardized test that students usually take before entering graduate...
The Graduate Record Examination (GRE) is a standardized test that students usually take before entering graduate school. An article reveals that the scores on the verbal portion of the GRE are (approximately) normally distributed with mean 462 points and standard deviation 119 points. (i) Find the 3rd decile for these scores. (ii) Find the probability that the scores are between 380 and 520 points.
Sophia who took the Graduate Record Examination (GRE) scored 167 on the Verbal Reasoning section and...
Sophia who took the Graduate Record Examination (GRE) scored 167 on the Verbal Reasoning section and 161 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section for all test takers was 155 with a standard deviation of 7.06, and the mean score for the Quantitative Reasoning was 151 with a standard deviation of 7.11. Suppose that both distributions are nearly normal. (a) What is Sophias Z-score on the Verbal Reasoning section? On the Quantitative Reasoning section? (b)...
Scores on the GRE. A college senior who took the Graduate Record Examination exam scored 580...
Scores on the GRE. A college senior who took the Graduate Record Examination exam scored 580 on the Verbal Reasoning section and 650 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section was 459 with a standard deviation of 114, and the mean score for the Quantitative Reasoning was 432 with a standard deviation of 148. Suppose that both distributions are nearly normal. Round calculated answers to 4 decimal places unless directed otherwise. 1.Write down the short-hand...
Sophia who took the Graduate Record Examination (GRE) scored 157 on the Verbal Reasoning section and...
Sophia who took the Graduate Record Examination (GRE) scored 157 on the Verbal Reasoning section and 162 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section for all test takers was 150 with a standard deviation of 7.2, and the mean score for the Quantitative Reasoning was 153 with a standard deviation of 7.64. Suppose that both distributions are nearly normal. (a) What is Sophias Z-score on the Verbal Reasoning section? On the Quantitative Reasoning section? (b)...
The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools....
The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students’ scores on the quantitative portion of the GRE follow a normal distribution. (Source: http://www.ets.org/.) Suppose a random sample of 10 students took the test, and their scores are given below. 152, 126, 146, 149, 152, 164, 139, 134, 145, 136 a) Test the claim that the mean verbal reasoning score is different from 150 at the α = 0.10 level of significance.
The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools....
The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students' scores on the quantitative portion of the GRE follow a normal distribution with standard deviation 8.8. Suppose a random sample of 10 students took the test, and their scores are given below. 152, 126, 146, 149, 152, 164, 139, 134, 145, 136 a. Are the criteria for approximate normality satisfied? Why? b. Calculate the sample mean, x with bar on top. Round your...
4. The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate...
4. The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students’ scores on the quantitative portion of the GRE follow a normal distribution. (Source: http://www.ets.org/.) Suppose a random sample of 10 students took the test, and their scores are given below. 152, 126, 146, 149, 152, 164, 139, 134, 145, 136 a) Test the claim that the mean verbal reasoning score is different from 150 at the α = 0.10 level of significance....
3. The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate...
3. The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students’ scores on the quantitative portion of the GRE follow a normal. (Source: http://www.ets.org/.) Suppose a random sample of 10 students took the test. 152, 126, 146, 149, 152, 164, 139, 134, 145, 136 A normal probability plot verifies that the data are normally distributed. a) Determine the sample standard deviation. b) Construct a 95% confidence interval for the population standard deviation. Interpret...
The Graduate Record Examination (GRE) is a standardized test commonly taken by graduate school applicants in...
The Graduate Record Examination (GRE) is a standardized test commonly taken by graduate school applicants in the United States. The total score is comprised of three compo- nents: Quantitative Reasoning, Verbal Reasoning, and Analytical Writing. The first two components are scored from 130 - 170. The mean score for Verbal Reasoning section for all test takers was 151 with a standard deviation of 7, and the mean score for the Quantitative Reasoning was 153 with a standard deviation of 7.67....
The Graduate Record Examination (GRE) is a standardized test commonly taken by graduate school applicants in...
The Graduate Record Examination (GRE) is a standardized test commonly taken by graduate school applicants in the United States. The total score is comprised of three compo- nents: Quantitative Reasoning, Verbal Reasoning, and Analytical Writing. The first two components are scored from 130 - 170. The mean score for Verbal Reasoning section for all test takers was 151 with a standard deviation of 7, and the mean score for the Quantitative Reasoning was 153 with a standard deviation of 7.67....
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT