Question

In: Statistics and Probability

1. The Graduate Management Admission Test (GMAT) is a test required for admission into many masters...

1. The Graduate Management Admission Test (GMAT) is a test required for admission into many masters of business administration (MBA) programs. Suppose a random sample of 8 students took the test, and their scores are given below. 699, 560, 414, 570, 521, 663, 727, 413

-Find a point estimate of the population mean -Construct and interpret a 95% confidence interval for the true mean score for the population.

-How many students should be surveyed to estimate the mean score within 25 points with 90% confidence?

-How many students should be surveyed to estimate the mean score within 25 points with 95% confidence?

-. How many students should be surveyed to estimate the mean score within 25 points with 99% confidence?

Solutions

Expert Solution

1)

Point estimate of population mean is the average of data points and obtained using the excel function =AVERAGE(),

The 95% confidence interval is,

where z-value is 1.96 for 95% confidence interval (obtained from z-distribution table for alpha=0.05) and SE is the standard error,

The standard deviation "s" is obtained using the excel function =STDEV() which gives s = 120.3678

Now,

2)

where z = 1.64 for 90% confidence interval, s = 120.3678

3)

Here z = 1.96 for 95% confidence interval

4)

Here z = 2.576 for 99% confidence interval

orchestra answered 2 years ago
Next > < Previous

Related Solutions

1. The Graduate Management Admission Test (GMAT) is a test required for admission into many masters...
1. The Graduate Management Admission Test (GMAT) is a test required for admission into many masters of business administration (MBA) programs. Total scores on the GMAT are normally distributed and historically had a population standard deviation of 113. The Graduate Management Admission Council (GMAC), who administers the test, claims that the mean total score is 529. Suppose a random sample of 8 students took the test and their scores are given below: 699, 560, 414, 570, 521, 663, 727, 413...
The Graduate Management Admission Test (GMAT) is a test required for admission into many masters of...
The Graduate Management Admission Test (GMAT) is a test required for admission into many masters of business administration (MBA) programs. Total scores on the GMAT are normally distributed. The Graduate Management Admission Council, who administers the test, claims that the mean total score is 580.   Suppose a random sample of 8 students took the test, and their scores are given below. 640 610 560 610 570 680 670 560 A. Use α = .05 to test the claim that the...
The Graduate Management Admission Test (GMAT) is a test required for admission into many Master of...
The Graduate Management Admission Test (GMAT) is a test required for admission into many Master of Business Administration (MBA) programs. Total scores on the GMAT are normally distributed. The Graduate Management Admission Council, who administers the test, claims that the mean total score is 579. (Source: http://www.mba.com/.) Suppose a random sample of 8 students took the test, and their scores are given below. 699, 560, 414, 570, 521, 663, 727, 413 At the 0.05 level of significance, test the claim...
The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part...
The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score is 547 (Magoosh website, January 5, 2015). Assume that GMAT scores are bell-shaped with a standard deviation of 100 . a. What percentage of GMAT scores are 647 or higher?    b. What percentage of GMAT scores are 747 or higher (to 1 decimal)?    c. What percentage of GMAT...
Suppose that test scores on the Graduate Management Admission Test (GMAT) are normally distributed with a...
Suppose that test scores on the Graduate Management Admission Test (GMAT) are normally distributed with a mean of 530 and standard deviation of 75. a. What GMAT score separates the highest 15% of the scores from the rest? Do not round intermediate calculations. Round your answer to the nearest whole number. GMAT score = b. What GMAT score corresponds to the 97 percentile? Do not round intermediate calculations. Round your answer to the nearest whole number. GMAT score = c....
The Graduate Management Admission Test (GMAT) has scores from 100 to 900. Scores are supposed to...
The Graduate Management Admission Test (GMAT) has scores from 100 to 900. Scores are supposed to follow a Normal distribution with a mean of 500 and standard deviation of 150. a. Suppose you earned a 800 on your GMAT test. From that information and the 68-95-99.7 Rule, where do you stand among all students who took the GMAT? b.Suppose you earned a 450 on your GMAT test. Where do you stand among all students who took the GMAT? c. Assuming...
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...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT