Grades on a standardized test are known to have a mean of 920 for students in th
ID: 3072658 • Letter: G
Question
Grades on a standardized test are known to have a mean of 920 for students in the United States. The test is administered to 449 randomly selected students in Florida; in this sample, the mean is 931.96 and the standard deviation (s) is 99.36. The 95% confidence interval for the average test score for Florida students is (922.77 , 941.15). (Round your responses to two decimal places.) Is there statistically significant evidence that Florida students perform differently than other students in the United States? The 95% confidence interval for the average test score for Florida students does not include 920, so the null hypothesis that -920 (that Florida students have the same average performance as other students in the United States) can be rejected at the 5% level. Another 499 students are selected at random from Florida. They are given a 3-hour preparation course before the test is administered. Their average test score is 937.48 with a standard deviation of 87.40 The 95% confidence interval for the change in average test score associated with the prep course is . (Round your responses to two decimal places.)Explanation / Answer
Ans:
(Assume population variances are equal)
pooled standard deviation=SQRT((448*99.36^2+498*87.4^2)/(449+499-2))=93.255
standard error=93.255*SQRT((1/449)+(1/499))=6.066
df=449+499-2=946
critical t value=tinv(0.05,946)=1.962
95% confidence interval for change in average scores
=(931.96-937.48)+/-1.962*6.066
=-5.52+/-11.90
=(-17.42, 6.38)
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