Question

In: Math

You may need to use the appropriate technology to answer this question. The College Board provided...

You may need to use the appropriate technology to answer this question.

The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514.† SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree.

College Grads
501 471
534 549
634 526
554 410
534 515
556 578
513 464
592 469
High School Grads
442 492
580 478
479 425
486 485
528 390
524 535

(a)

Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education. (Let μ1 = population mean verbal score of students whose parents are college graduates with a bachelor's degree and μ2 = population mean verbal score of students whose parents are high school graduates but do not have a college degree.) For purposes of this study, assume the population variances are unequal when conducting the t-test.

H0: μ1μ2 < 0

Ha: μ1μ2 = 0

H0: μ1μ2 = 0

Ha: μ1μ2 ≠ 0

     

H0: μ1μ2 ≠ 0

Ha: μ1μ2 = 0

H0: μ1μ2 ≥ 0

Ha: μ1μ2 < 0

H0: μ1μ2 = 0

Ha: μ1μ2 > 0

(b)

What is the point estimate of the difference between the means for the two populations?

(c)

Find the value of the test statistic. (Round your answer to three decimal places.)

Compute the p-value for the hypothesis test. (Round your answer to four decimal places.)

p-value =

(d)

At

α = 0.05,

what is your conclusion?

Do not reject H0. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.Do not Reject H0. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.      Reject H0. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.Reject H0. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.

Solutions

Expert Solution

From the given information,

H0: μ1μ2 = 0

Ha: μ1μ2 > 0

Using Minitab:

  • .Choose Stat > Basic Statistics > 2-Sample t.
  • Choose Samples in different columns.
  • In First, enter the column of college.
  • In Second, enter the column of High school.
  • Choose Options.
  • In Confidence level, enter 95.
  • In Alternative, select greater than.
  • Click OK in all the dialog boxes

Follow the above instructions to find the following output.

From the output, the P-value is 0.037

Part d.

The p-value 0.037 is less than level of significance 0.05

.Reject H0. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.

Hope this will be helpful. Thanks and God Bless You:)


Related Solutions

You may need to use the appropriate technology to answer this question. As part of a...
You may need to use the appropriate technology to answer this question. As part of a study designed to compare hybrid and similarly equipped conventional vehicles, a group tested a variety of classes of hybrid and all-gas model cars and sport utility vehicles (SUVs). Suppose the following data show the miles-per-gallon rating obtained for two hybrid small cars, two hybrid midsize cars, two hybrid small SUVs, and two hybrid midsize SUVs; also shown are the miles per gallon obtained for...
you may need to use the appropriate technology to answer this question. To study the effect...
you may need to use the appropriate technology to answer this question. To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow. Temperature 50°C 60°C 70°C 33 30 24 23 30 29 35 34 27 39 24 29 30 27 36 Construct an analysis of variance table. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.)...
You may need to use the appropriate appendix table or technology to answer this question. In...
You may need to use the appropriate appendix table or technology to answer this question. In the past, 19% of all homes with a stay-at-home parent had the father as the stay-at-home parent. An independent research firm has been charged with conducting a sample survey to obtain more current information. (a) What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home...
You may need to use the appropriate appendix table or technology to answer this question. The...
You may need to use the appropriate appendix table or technology to answer this question. The following results are for independent random samples taken from two populations. Sample 1 Sample 2 n1 = 20 n2 = 30 x1 = 22.9 x2 = 20.1 s1 = 2.6 s2 = 4.6 (a) What is the point estimate of the difference between the two population means? (Use x1 − x2. ) (b) What is the degrees of freedom for the t distribution? (Round...
You may need to use the appropriate technology to answer this question. Scores in the first...
You may need to use the appropriate technology to answer this question. Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in golf tournaments are shown in the following table. Player First Round Final Round Golfer 1 70 72 Golfer 2 71 72 Golfer 3 70 73 Golfer 4 72 71 Golfer 5 70 69 Golfer 6 67 67 Golfer 7 71 68 Golfer 8 68 74 Golfer 9 67 73 Golfer 10...
You may need to use the appropriate technology to answer this question. Scores in the first...
You may need to use the appropriate technology to answer this question. Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in golf tournaments are shown in the following table. Player First Round Final Round Golfer 1 70 72 Golfer 2 71 72 Golfer 3 70 73 Golfer 4 72 71 Golfer 5 70 69 Golfer 6 67 67 Golfer 7 71 67 Golfer 8 68 74 Golfer 9 67 72 Golfer 10...
You may need to use the appropriate technology to answer this question. Scores in the first...
You may need to use the appropriate technology to answer this question. Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in golf tournaments are shown in the following table. Player First Round Final Round Golfer 1 70 72 Golfer 2 71 72 Golfer 3 70 75 Golfer 4 72 71 Golfer 5 70 69 Golfer 6 67 67 Golfer 7 71 67 Golfer 8 68 72 Golfer 9 67 71 Golfer 10...
You may need to use the appropriate appendix table or technology to answer this question. A...
You may need to use the appropriate appendix table or technology to answer this question. A report states that adults 18- to 24- years-old send and receive 128 texts every day. Suppose we take a sample of 25- to 34- year-olds to see if their mean number of daily texts differs from the mean for 18- to 24- year-olds. (a) State the null and alternative hypotheses we should use to test whether the population mean daily number of texts for...
You may need to use the appropriate appendix table or technology to answer this question. The...
You may need to use the appropriate appendix table or technology to answer this question. The following results come from two independent random samples taken of two populations. Sample 1 Sample 2 n1 = 50 n2 = 35 x1 = 13.6 x2 = 11.6 σ1 = 2.5 σ2 = 3 Provide a 90% confidence interval for the difference between the two population means. (Use x1 − x2.Round your answers to two decimal places.) ( ) to ( ) Provide a...
You may need to use the appropriate appendix table or technology to answer this question. The...
You may need to use the appropriate appendix table or technology to answer this question. The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed (Time.com). The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars. Private Colleges 53.8 44.2 45.0 32.3 45.0 31.6 46.8 37.8 49.5 43.0 Public Colleges 20.3 22.0 28.2 15.6 24.1 28.5 22.8 25.8 18.5 25.6 14.4 21.8...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT