Question

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

a. Find a point estimate of the population mean.

b. Write a sentence about how you can verify the data could come from a population that is normally distributed, using the graph below.

Normal Quante

c. Construct and interpret a 95% confidence interval for the true mean score for the population.

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

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

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

2. A group of Brigham Young University—Idaho students (Matthew Herring, Nathan Spencer, Mark Walker and Mark Steiner) collected data on the speed of vehicles traveling through a construction zone on a state highway, where the posted speed was 25 mph. The recorded speed (in mph) of 14 randomly selected vehicles is given below.

20, 24, 27, 28, 29, 30, 32, 33, 34, 36, 38, 39, 40, 40

a. Assuming speeds are approximately normally distributed, construct a 95% confidence Interval for the true mean speed of drivers in this construction zone. Interpret the Interval.

b. Construct a 99% confidence interval for the true mean speed of drivers in this construction zone. Interpret the interval.

c. Compare the widths of the 95% and 99% confidence Intervals.

d. What conclusions do you draw about the speeds people drive in this construction zone?

3. It has been reported that the probability that an individual will develop schizophrenia over their lifetime is 0.004. In a random sample of 3000 individuals, it was determined that 17 developed schizophrenia. Is there evidence to support the claim that the true proportion of people who will develop schizophrenia is different from 0.004 at the 0.05 level of significance? (Source: Saha S, Chant D, Welham J, McGrath J. A systematic review of the prevalence of schizophrenia. PLOS Med 2(5): e141.)

a. State your null and alternative hypothesis:

b. Describe what you type into your calculator to have it run the numbers.

c. State your P-value

d. State your conclusion is a way a non-stat student would understand.

4. 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 529. (Source: 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

Does the sample evidence suggest the mean total score is different from 529 at the 0.05 level of significance?

a. State your null and alternative hypothesis:

b. Describe what you type into your calculator to have it run the numbers.

c. State your P-value

d. State your conclusion is a way a non-stat student would understand.

5. 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.

www.ets.org) Suppose a random sample of 10 economics students took the test, and their scores are given below.

158, 166, 158, 149, 154, 164, 169, 144, 155, 160

Test the claim that the mean quantitative score is greater than 152.1 at the 0.10 level of significance.

a. State your null and alternative hypothesis:

b. Describe what you type into your calculator to have it run the numbers.

c. State your P-value

d. State your conclusion is a way a non-stat student would understand.

6. In a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement. Does the sample evidence suggest that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement? Answer the following:

a. What would it mean to make a Type II error for this test?

b. If the researcher decides to test this hypothesis at the 0.05 level of significance, determine the probability of making a Type II error if the true population proportion is 0.54. What is the power of the test?

Please can you number the answers back to me.

Answer 1

1.

a) From the given data

a) From the given data Descriptive Statistics: Sample Variable sample Total count Mean StDev Variance 8 570.9 120.4 14488.4 a) Point estimate of the population mean is 570.9 b) The points are closed to straight line so it follows normal distribution c) Descriptive Statistics: Sample Variable sample Total count Mean StDev Variance 8 570.9 120.4 14488.4 c) The number of students should be surveyed to estimate the mean score within 25 points with 90% confidence is d) Given, 90% confidence interval, s = 120.4, M.E.=25 sample size(n) = t^2_alpha/2,n-ldf s^2/M.E.^2 = (t_0.10/2,8-1-ldf)^2 (120.4)^2/25^2 = 0.895^2(120.4)^2/25^2 = 84 e) Given, 95% confidence interval, s = 120.4, M.E.=25 sample size(n) = t^2_alpha/2,n-ldf s^2/M.E.^2 = (t_0.05/2,8-1-ldf)^2(120.4)^2/25^2 = 2.365^2(120.4)^2/25^2 = 130 f) Given, 99% confidence interval, s = 120.4, M.E.=25 sample size(n) = t^2_alpha/2,n-ldf s^2/M.E.^2 = (t_0.01/2,8-1-ldf)^2(120.4)^2/25^2 = 3.5^2(120.4)^2/25^2 = 285

a) Point estimate of the population mean is 570.9

b) The points are closed to straight line so it follows normal distribution

c)

c) The number of students should be surveyed to estimate the mean score within 25 points with 90% confidence is