A test has been developed to measure the attitudes of executives of a large company towards minorities. A high score indicates a negative attitude and a low score indicates a positive attitude. Independent random samples of 25 male and 16 female executives were drawn. For the former group, the sample mean and sample standard deviation of the scores are 85.8 and 19.13, respectively; while for the latter they are 71.5 and 12.2, respectively. Assume that the test score follows a normal distribution with unknown but equal variances. a) Use the sample to check whether there is evidence to conclude that the attitude toward minorities is more positive among female executives compared to male executives. Use a significance of 5%. b) Find the p-value of the test. c) Check if the assumption of unknown but equal variances was correct. Use a significance of 5%.
A test has been developed to measure the attitudes of executives of a large company towards minorities. A high score indicates a negative attitude and a low score indicates a positive attitude. Independent random samples of 25 male and 16 female executives were drawn. For the former group, the sample mean and sample standard deviation of the scores are 85.8 and 19.13, respectively; while for the latter they are 71.5 and 12.2, respectively. Assume that the test score follows a
a) Use the sample to check whether there is evidence to conclude that the attitude toward minorities is more positive among female executives compared to male executives. Use a significance of 5%.
b) Find the p-value of the test.
c) Check if the assumption of unknown but equal variances was correct. Use
a significance of 5%.
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