A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago.A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken.You are given the following information. The p-value for the difference between the two population means is

A) .0013.
B) .0027.
C) .4987.
D) .9987.

Question

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago.A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken.You are given the following information.

The p-value for the difference between the two population means is

A) .0013.
B) .0027.
C) .4987.
D) .9987.

Sabrina Veasy · Accepted Answer

Final Answer : B, Explanation :  The p-value is the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true. If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis in favor of the alternative hypothesis.Since the p-value is less than 0.05, we can conclude that there is a statistically significant difference in the abilities of students enrolled in statistics today and those enrolled five years ago.Choice A is incorrect because .0013 is less than 0.001, which is not a typical significance level used in hypothesis testing.Choice C is incorrect because the p-value is less than 0.5, which would indicate statistical significance if the significance level were set to 0.5, but it's not a common significance level.Choice D is incorrect because a p-value of 0.9987 would indicate we fail to reject the null hypothesis, meaning there is no statistically significant difference between the two groups, which is in contrast to the given information.

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