Question

Do students who learned English and another language simultaneously score worse on the SAT Critical Reading exam than the general population of test takers? The mean score among test takers on the SAT Critical Reading exam is 501. A random sample of 100 test takers who learned English and another language simultaneously had a mean SAT Critical Reading score of 485 with a standard deviation of 116. Do these results suggest that students who learn English as well as another language simultaneously score worse on the SAT Critical reading exam? Use the α=0.5 level of significance.

1. a) State the null and alternative hypothesis.

2. b) Verify that the requirements.

3. c) Calculate the test statistic.

4. d) Find the corresponding P‐value.

5. e) State your conclusion.

Answer 1

Given: = 501, s = 116, = 485, n = 100, = 0.05

(a) The Hypothesis:

H0: = 501

Ha: < 501

This is a Left Tailed Test.

(b) Requirements

(1) Sample size is > 30, so we assume that the distribution is approximately normal

(2) The sample is a simple randome sample

(3) Samples are independent of each other

(c) The Test Statistic: Since the population standard deviation is unknown, we use the students t test .

The test statistic is given by the equation:

(e) The p Value: The p value for t = -1.38, df = n - 1 = 99 is; p value = 0.0853

(f) Since p value is >

Fail to Reject H0. there isn't sufficient evidence at the 95% level of significance to conclude that students who learnt English as well as another language simultaneously scored worse on the SAT critical reading exam.

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