Question 2. A researcher was interested in whether understanding of statistics could be improved as a result of taking a statistics course. The researcher knew that the population average Understanding of Statistics (UOS) score was 10, but the population standard deviation was unknown. The researcher gathered a sample of five students who then took a short course on statistics. At the end of the course, the students were given the same UOS survey. The researcher obtained the following results: Anthony 11 Jasper 14 Ann 9 Margaret 13 Sam 12 a) Test the researcher’s hypothesis using a significant a-level of 0.05 (4 steps) b) If the researcher’s increases the significant a-level to 0.01, would the researcher make the same conclusion? What is the conclusion now? Why? c) If the researcher increases the sample size from 5 students to 10 students with sample mean of 12 and sample standard deviation of 2, would the researcher make the same conclusion at 0.01 significant level? What is the conclusion now? Why?
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.
Question 2. A researcher was interested in whether understanding of statistics could be improved as a result of taking a statistics course. The researcher knew that the population average Understanding of Statistics (UOS) score was 10, but the population standard deviation was unknown. The researcher gathered a sample of five students who then took a short course on statistics. At the end of the course, the students were given the same UOS survey. The researcher obtained the following results:
Anthony 11 Jasper 14
Ann 9 Margaret 13 Sam 12
a) Test the researcher’s hypothesis using a significant a-level of 0.05 (4 steps)
b) If the researcher’s increases the significant a-level to 0.01, would the researcher make the same conclusion? What is the conclusion now? Why?
c) If the researcher increases the sample size from 5 students to 10 students with sample mean of 12 and sample standard deviation of 2, would the researcher make the same conclusion at 0.01 significant level? What is the conclusion now? Why?
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