According to the norms established for a reading comprehension test, eighth graders should average 84.3 with a standard deviation of 8.6. If 45 randomly selected eighth graders from a certain school district averaged 87.8, use the four steps below to test the null hypothesis μ=84.3 against the alternative μ>84.3 at the 0.01 level of significance. 1. Formulate H0 and H1, and specify α. 2. Using the sampling distribution of an appropriate test statistic, determine a critical region of size α. 3. Determine the value of the test statistic from the sample data. 4. Check whether the value of the test statistic falls into the critical region and, accordingly, reject the null hypothesis, or reserve judgment. (Note that we do not accept the null hypothesis because β, the probability of false acceptance, is not specified in a test of significance.)
According to the norms established for a reading comprehension test, eighth graders should average 84.3 with a standard deviation of 8.6. If 45 randomly selected eighth graders from a certain school district averaged 87.8, use the four steps below to test the null hypothesis μ=84.3 against the alternative μ>84.3 at the 0.01 level of significance.
1. Formulate H0 and H1, and specify α.
2. Using the sampling distribution of an appropriate test statistic, determine a critical region of size α.
3. Determine the value of the test statistic from the sample data.
4. Check whether the value of the test statistic falls into the critical region and, accordingly, reject the null hypothesis, or reserve judgment. (Note that we do not accept the null hypothesis because β, the probability of false acceptance, is not specified in a test of significance.)
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