Question

In: Statistics and Probability

The College Board provided comparisons of SAT scores based on the highest level of education attained...

The College Board provided comparisons of 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. This data set contains verbal SAT scores for a sample of students whose parents are college graduates and a sample of students whose parents are high school graduates. Use 0.01 as your level of significance.

  1. Formulate hypotheses to test the research hypothesis. Let population 1 be the students whose parents are college graduates and let population 2 be students whose parents are high school graduates.
  2. Is this an one-tailed or two-tailed test?
  3. Use Excel to test your hypotheses. What is the test statistic?
  4. What is the p-value?
  5. What is the critical value?
  6. What is your conclusion using 0.01 as the level of significance?
  7. Explain your conclusion in the context of the problem (i.e. in terms a non-statistician could understand).
College High School
485 442
534 580
650 479
554 486
550 528
572 524
497 492
592 478
487 425
533 485
526 390
410 535
515
578
448
469
College High School
485 442
534 580
650 479
554 486
550 528
572 524
497 492
592 478
487 425
533 485
526 390
410 535
515
578
448
469

Solutions

Expert Solution

using excel>addin>phsatat>two sample test

we have

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference 0
Level of Significance 0.01
Population 1 Sample
Sample Size 16
Sample Mean 525
Sample Standard Deviation 59.4
Population 2 Sample
Sample Size 12
Sample Mean 487
Sample Standard Deviation 51.7
Intermediate Calculations
Population 1 Sample Degrees of Freedom 15
Population 2 Sample Degrees of Freedom 11
Total Degrees of Freedom 26
Pooled Variance 3166.4304
Standard Error 21.4889
Difference in Sample Means 38.0000
t Test Statistic 1.7684
Upper-Tail Test
Upper Critical Value 2.4786
p-Value 0.0444
Do not reject the null hypothesis
  1. this is one-tailed test.
  2. \the test statistic is 1.7684
  3. the p-value is 0.0444
  4. the critical value is 2.4786
  5. Do nit reject Ho beacsue the value of test statistic is less than 2.4786
  6. we dont have sufficient evidance to conclude that parents who had attained a higher level of education would on average score higher on the SAT

orchestra answered 2 years ago
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