tate 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 standardized evaluation technique. The average score for the sample if M = 76. For the general population of college students, writing scores form a normal distribution with a mean of μ= 70. If the writing scores for a population have a standard deviation of σ = 20, does the sample provide enough evidence to conclude that the new composition course has a significant effect? Assume a two-tailed test with α = .05. If the population standard deviation is = 10, is the sample sufficient to demonstrate a significant effect? Again, assume a two-tailed test with α = .05. Comparing your answers for parts a and b, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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 standardized evaluation technique. The average score for the sample if M = 76. For the general population of college students, writing scores form a
- If the writing scores for a population have a standard deviation of σ = 20, does the sample provide enough evidence to conclude that the new composition course has a significant effect? Assume a two-tailed test with α = .05.
- If the population standard deviation is = 10, is the sample sufficient to demonstrate a significant effect? Again, assume a two-tailed test with α = .05.
- Comparing your answers for parts a and b, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.
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