For items 27 to 29: Aprofessor wants to determine whether thereis a difference in the final averages between the past two semesters of his business statistics dasses. For a random sample of 16 students from semester 1, the mean of the final averages was 75 with standard deviation of 4. For arandom sample of 9 students from semester 2, the mean was 73 with standard deviation of 6. 27. If the final averages from semester 1 and 2 are assumed to be normally dstributed with equal variances. Which ofthe following is the appropriate set of hypotheses? A Ho: Ha - Hz S0 vs Ha: -Hz > 0 B. Ho: la - H2 20 vs HA: a-H2 <0 C Hoi - Hz = 0 vs Ha: - Ha # 0 D. Ho: - Hz 0 vs Ha: -z = 0 28. What is the computed test statistics for the appropriate test? A z = 2.0889 29. What is the correct decision forthe appropriate test at a 0.05level of significance when the population variances are assumed to be equal? A Do notreject the null hypothesis. B. t = 1.002 C t = 2.0889 D. z= 0.8944 C. Reject the altemate hypothesis D Do not roioct the altem ate hmothesis.
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.
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