Question

Do ESL students score lower in English college placement tests than the national average? A researcher obtained the English placement test scores of a random sample of 53 ESL students. He finds that the mean score of these 53 students is 147.9. Is this significantly different from the national average (u = 150, 0 = 15)? Using a = .05, match the correct answers to each value N 53 Zobserved < - 1.02 Zcv -1.65 Standard error of the mean 2.06 <

Answer 1

The null hypothesis is

H:H= 150

The alternate hypothesis is

$H_{a} : \mu < 150$

The observed test statistics is

z = -1.02

The critical value of Z is = -1.65

Since the observed value is not more extreme than the critical value hence we will accept the null hypothesis.

Moreover, the p-value corresponding to a z-score of -1.02 is 0.1539.

The significance level alpha is = 0.05 which is less than the significance level. Hence, by this method also we can conclude that we would fail to reject the null hypothesis.

Conclusion: Fail to reject the null hypothesis.

Result Interpretation: There is not sufficient evidence to conclude that the ESL students score lower in English college placement tests than the national average.

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