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Statistics: College Writing Scores

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State college is evaluating a new english composition course for freshmen. A random sample of N=25 freshmen is obtained and the students are placed in the course during their first semester. One year later, a writing sample is obtained for each student and the writing samples are graded using a standard evaluation technique. The average score for the sample is m=76. For the general population of college students, writing scores form a normal distribution of m = 70.

A. If the writing scores for the population have a standard deviation of 20, does the sample provide enough evidence to conclude that the new composition course has a significant effect? Assume a two tailed test with alpha level of 0.05.

B. If the population standard deviation is 10 , is the sample sufficient to demonstrate a significant effect? Again assume a two tailed test with alpha level of 0.05.

C. comparing your answer for parts a and b explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.

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Null Hypothesis: The new composition course does not have a significant effect.
Ho: u = 70.
Alternate Hypothesis: The new composition course has a significant effect.
H1: u does not equal 70.

Analysis ...

Solution provided by:
Anwesha Ghosh, MSc
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  • MSc, Osmania University
  • MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
  • BSc, Banaras Hindu University
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