A researcher has a sample of 600 observations from a population whose standard deviation is known to be 51.44. The mean of the sample is calculated to be 3.6.
The null hypothesis is stated as Ho: mean > 8.4. The researcher should
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A. B. C. D.Explanation
To test the hypothesis, you need to calculate the largest z-statistic since the null hypothesis is unidirectional and to the right. This makes it the hardest to reject the null and you should always use the most stringent criterion for rejecting the null. After all, the null is the hypothesis maintained to be true by default and only a sufficient weight of evidence should be used to reject that view. The largest z-statistic calculated under the null hypothesis is equal to (3.6 - 8.4)/2.1 = -2.4. Now, the alternative hypothesis is H1: mean <= 8.4. Since the alternative is directional, we use a one-tailed test. For this, the critical value at 95% level is -1.645 and for
99%, it is -2.32. -2.32 is the value below which only 1% of the probability mass of the standard normal distribution lies. Similarly, only 5% of probability lies below -
1.645). Since even the calculated z-statistic that is most favorable to the null lies in the rejection region, we can reject the null at the 99% level in a one-sided test.