Claire is an educational researcher looking to determine the relative effectiveness of two different teaching methods on standardized test scores. A group of high school seniors is taught using a traditional method, while a second group is taught using an experimental method. Claire selects a random sample of 10 students from each group and records the standardized test score for each student, as shown in the following table. Assume that the population standard deviation of test scores is 6 points for the traditional group and 11 points for the experimental group, and assume that the test scores for both groups are normally distributed. Let the standardized test scores of students taught using the traditional method be the first sample, and let the standardized test scores of students taught using the experimental method be the second sample. At the 0.10 level of significance, is there evidence of a difference in test scores between the students taught using the two methods? Perform the test using a TI-83, TI-83 Plus, or TI-84 calculator. Find the test statistic, rounded to two decimal places, and the p-value, rounded to three decimal places.
Traditional Experimental
99
117
89
76
104
97
95
96
90
121
109
91
98
84
95
115
100
89
101
103
Z & P-value = ?