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.
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.