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Conscientiousness is a tendency to show self-discipline, act dutifully, and aim for achievement. The trait shows a preference for planned rather than spontaneous behavior. A random sample of 650 students is asked to fill out the Hogan Personality Inventory (HPI) to measure their level of conscientiousness. The 300 undergraduate students scored an average of 148 with a standard deviation of 16. The 350 graduate students had a mean score of 153 with a standard deviation of 21. Is this enough evidence to conclude that graduate students score higher, on average, on the HPI than undergraduate students?
-What is the value of the test statistic for testing these hypotheses using a pooled two sample t-test?
A) 0.27
B) 3.37
C) 3.44
D) 6.89

Question

Use the following information for questions:
 Conscientiousness is a tendency to show self-discipline, act dutifully, and aim for achievement. The trait shows a preference for planned rather than spontaneous behavior. A random sample of 650 students is asked to fill out the Hogan Personality Inventory (HPI) to measure their level of conscientiousness. The 300 undergraduate students scored an average of 148 with a standard deviation of 16. The 350 graduate students had a mean score of 153 with a standard deviation of 21. Is this enough evidence to conclude that graduate students score higher, on average, on the HPI than undergraduate students?
-What is the value of the test statistic for testing these hypotheses using a pooled two sample t-test?
A) 0.27
B) 3.37
C) 3.44
D) 6.89

Quizplus · Accepted Answer

The test statistic for a pooled two-sample t-test can be calculated using the formula for the difference between two sample means, taking into account the pooled standard deviation and the sizes of both samples. Given the provided means, standard deviations, and sample sizes for undergraduate and graduate students, the calculation results in a test statistic value that closely matches option B (3.37), indicating a significant difference between the two groups' average scores on the HPI.

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