Suppose a group of high school students (n=200) take a standardized test; the me

Question

Suppose a group of high school students (n=200) take a standardized test; the mean score for this group is = 460. The general population mean and standard deviation for this particular test are µ = 445 and = 100. The researcher is interested in testing the research hypothesis that this sample of students has a higher mean than the general population (i.e., this sample of students comes from a population that has a higher mean than the general population). He chooses a Type I error rate of .01.

Is the researcher testing a directional or nondirectional hypothesis?

Calculate the p-value and make a decision about whether to reject or accept the null hypothesis.

Explanation / Answer

The researcher is testing a directional hypothesis because there is an attempt to establish whether the sample mean is higher than the population mean. If it were non-directional, the research question would’ve just predicted a difference, rather than stating the direction of the difference.

The result was found to be significant at the 0.01 level ( P = 0.0351 ). Based on this finding, we can reject the null hypothesis.

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