5) The International English Language Testing System (IELTS) has six modules, on

Question

5) The International English Language Testing System (IELTS) has six modules, one of which assesses listening skills. IELTS researchers reported that a recent mean for everyone who completed this module in one year was 6.00 and the standard deviation was 1.30 (2013). A sample of 63 international students who were accepted to study at the University of Melbourne in Australia had mean IELTS listening scores of 7.087 with a standard deviation of 0.754 (O’Loughlin & Arkoudis, 2009). Show your work

a. Calculate the 95% confidence interval for this sample.

b. State in your own words what we learn from this confidence interval.

c. What information does the confidence interval provide that we also get from a hypothesis test?

Explanation / Answer

a)

CI for University of Melbourne admits

Mean = 7.087

SD = 0.754

N= 63

At 95% CI, z=1.96

CI = Mean +- z*SD/sqrt (N)

= 7.087 +- 1.96*0.754/sqrt (63)

= 7.087 +- 0.186

= (6.9, 7.273)

b)

It says that there is a 95% chance that the admits in that university will have a IELTS score in the CI

c)

If the mean value is in the CI, then we cannot reject the null hypothesis

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