Question

Question 9 10 pts Suppose that for a given year, the mean score on the SAT Mathematics Test was 515. The data is assumed to be normally distributed and the population standard deviation is 100. Is there sufficient evidence, at the 0.10 level of significance, to determine if the mean score of 36 SAT scores is less than the mean score for that given year? The 36 SAT scores are listed below as follows: 496 506 507 505 438 499 505 522 531 762 513 493 522668 543 519 349 506 519 516 714 517 511 551 287 523 576 516 515 500 243 509 523 503 414 504 The rejection region is Z < -Za/2 = -1.28 True False

Answer 1

Let, Xi = ith SAT score of mathematics test

We formulate the null hypothesis and alternative hypothesis.

Hou = 515 and H:u <515

Here,

n= Sample size = 36

u = Hypothesized mean = 515

Population standard deviation 100

36 i=1X, Ν 509.0278 n

The test statistic is,

z = X-509.0278 - 515 o/ vn 100/136 -0.35833

Level of significance = 0.10

Here critical region is,

*z->z

-Za = -1.28

Z= -0.35833 >-Za = -1.28, hence we fail to reject Ho.

Conclusion: The mean score of 36 SAT scores is equal to the mean score for that given year i.e. 515.