Question

Consider the following hypothesis testing problem H0 : ? = ?0, H1 : ? ? ?0 (?=0.05). A data set of sample size 10 is collected. It is assumed that the variance is known, and the Z-test suggests that the null hypothesis is not rejected. Then, which of the following statement can possibly be true ? a). If a smaller value of ? is chosen (say, ? = 0.01), then, there is chance that the null hypothesis might be rejected based on the new ?. b). If a new data set of sample size 10 is collected and | ?? – ?0 | based on the new dataset is smaller than that of the old data set, then, there is a chance that the null hypothesis might be rejected based on the new data set. c). If a new data set of sample size 20 is collected and the sample mean remains approximately the same. Then, there is a chance that the null hypothesis might be rejected based on the new data set. d). None of the above statement is true.

          Consider the following hypothesis testing problem H0 : ? = ?0, H1 : ? ? ?0 (?=0.05). A data set of sample size 10 is collected. It is assumed that the variance is known, and the Z-test suggests that the null hypothesis is not rejected. Then, which of the following statement can possibly be true ?

a). If a smaller value of ? is chosen (say, ? = 0.01), then, there is chance that the null hypothesis might be rejected based on the new ?.
b). If a new data set of sample size 10 is collected and | ?? – ?0 | based on the new dataset is smaller than that of the old data set, then, there is a chance that the null hypothesis might be rejected based on the new data set.
c). If a new data set of sample size 20 is collected and the sample mean remains approximately the same. Then, there is a chance that the null hypothesis might be rejected based on the new data set.
d). None of the above statement is true.

Consider the following hypothesis testing problem H0 : ? = ?0, H1 : ? ? ?0 (?=0.05). A data set of sample size 10 is collected. It is assumed that the variance is known, and the Z-test suggests that the null hypothesis is not rejected. Then, which of the following statement can possibly be true ?

a). If a smaller value of ? is chosen (say, ? = 0.01), then, there is chance that the null hypothesis might be rejected based on the new ?.
b). If a new data set of sample size 10 is collected and | ?? – ?0 | based on the new dataset is smaller than that of the old data set, then, there is a chance that the null hypothesis might be rejected based on the new data set.
c). If a new data set of sample size 20 is collected and the sample mean remains approximately the same. Then, there is a chance that the null hypothesis might be rejected based on the new data set.
d). None of the above statement is true.

Added by Tammy W.

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