Question

olo SAT coaching: A sample of 10 students took a class designed to improve their SAT math scores. Following are their scores before and after the class. Can you conclude that the mean increase in scores is greater than 15 points? Let , represent the mean score after the class and Md = H, -Hz. Use the a=0.01 level and the P-value method with the TI-84 Plus calculator. Score Before 451 453 526 440 After 529 466 447 440 439 435 491 473 482 479 451 431 454 463 511 493 Send data to Excel Part 1 of 4 (a) State the appropriate null and alternate hypotheses. HO: M = 15 H: M, >15 This is a right-tailed test. Part: 1/4 Part 2 of 4 (b) Compute the P-value. Round the answer to at least four decimal places. P-value = 0.8869 х 5

Answer 1

Solution :

Mean d=16.4

Standard deviation =Sd=14.183

Sample size n=10

Let $\mu$ ₁ be the mean score after the test and

let $\mu$ ₂ be the mean score before the test.

Hence, represents the improvement of score after taking the test.

211 Inl Pn

Hence, the Null Hypothesis: H₀: the difference between the scores after taking the test and before taking the test is equal to 15 marks.

Alternate Hypothesis:H₁ : the difference between the scores after taking the test and before taking the test is more than 15 marks.

i.e.

H₀ :

P11 = M1 H2 = 15

H₁ :

15 12 111 = P11

Test statistic = (16.4-15)/(14. 183/sq(10)) =0.312

Degrees of freedom df= n-1=9

Significance level =0.01

P value = 0.3811

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