David Anderson has been working as a lecturer at Michigan State University for the last three years. He teaches two large sections of introductory accounting every semester. While he uses the same lecture notes in both sections, his students in the first section outperform those in the second section. He believes that students in the first section not only tend to get higher scores, they also tend to have lower variability in scores. David decides to carry out a formal test to validate his hunch regarding the difference in average scores. In a random sample of 18 students in the first section, he computes a mean and a standard deviation of 77.4 and 10.8, respectively. In the second section, a random sample of 14 students results in a mean of 74.1 and a standard deviation of 12.2. Sample 1 consists of students in the first section and Sample 2 represents students in the second section. a. Construct the null and the alternative hypotheses to test David’s hunch. multiple choice 1 H0: μ1 − μ2 = 0; HA: μ1 − μ2 ≠ 0 H0: μ1 − μ2 ≥ 0; HA: μ1 − μ2 < 0 H0: μ1 − μ2 ≤ 0; HA: μ1 − μ2 > 0 b-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic ? b-2. What assumption regarding the population variances is used to conduct the test? multiple choice 2 Known population standard deviations. Unknown population standard deviations that are equal. Unknown population standard deviations that are not equal. c. Implement the test at α = 0.01 using the critical value approach. multiple choice 3 Reject H0; there is evidence that scores are higher in the first section. Reject H0; there is no evidence that scores are higher in the first section. Do not reject H0; there is evidence that scores are higher in the first section. Do not reject H0; there is no evidence that scores are higher in the first section.
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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David Anderson has been working as a lecturer at Michigan State University for the last three years. He teaches two large sections of introductory accounting every semester. While he uses the same lecture notes in both sections, his students in the first section outperform those in the second section. He believes that students in the first section not only tend to get higher scores, they also tend to have lower variability in scores. David decides to carry out a formal test to validate his hunch regarding the difference in average scores. In a random sample of 18 students in the first section, he computes a mean and a standard deviation of 77.4 and 10.8, respectively. In the second section, a random sample of 14 students results in a mean of 74.1 and a standard deviation of 12.2. |
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Sample 1 consists of students in the first section and Sample 2 represents students in the second section. |
| a. |
Construct the null and the alternative hypotheses to test David’s hunch. |
multiple choice 1
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| b-1. |
Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) |
| Test statistic | ? |
| b-2. | What assumption regarding the population variances is used to conduct the test? |
multiple choice 2
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| c. | Implement the test at α = 0.01 using the critical value approach. |
multiple choice 3
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Introduction:
Denote μ1, μ2 as the true mean scores of students in the first and second sections, respectively. It is of interest to test the claim that the students in the first section tend to get higher scores.
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