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[32pts] X~NORM(44.0, 3.2). A sample mean of 43.7 is observed, for n=32. Given H0: ?=44.0, H1: ? < 44.0, and ?=0.05. This is a test on the mean for a single population. a. What test statistic should be used? (Z, T, ?², F?)? Why? b. What is the critical value of the test statistic to use for this test? What is the accept region (accept H0) and reject region (reject H0)? c. Based on the critical value, what is your conclusion regarding this test given the sample mean above? d. What impact would decreasing ? (say to 0.01) have on the critical value? On the test? What does ? control? e. What is the one-sided p-value for the sample mean above? f. Based on the p-value from part (e), what is your conclusion regarding this test given the sample mean above? Is it different than from part (c)? g. Suppose you are instead doing a two-sided test: Given H0: ?=44.0, H1: ? <> 44.0 and ?=0.05. Calculate the test critical values and state the conclusion of the test for the sample mean above. h. Supposed that, unknown to you, the distribution of X had shifted to ~NORM(42.8, 3.3). For n=30, calculate power and ? (type II error) for the two-sided hypothesis test of part (g).

          [32pts] X~NORM(44.0, 3.2). A sample mean of 43.7 is observed, for n=32. Given H0: ?=44.0, H1: ? < 44.0, and ?=0.05. This is a test on the mean for a single population.
a. What test statistic should be used? (Z, T, ?², F?)? Why?
b. What is the critical value of the test statistic to use for this test? What is the accept region (accept H0) and reject region (reject H0)?
c. Based on the critical value, what is your conclusion regarding this test given the sample mean above?
d. What impact would decreasing ? (say to 0.01) have on the critical value? On the test? What does ? control?
e. What is the one-sided p-value for the sample mean above?
f. Based on the p-value from part (e), what is your conclusion regarding this test given the sample mean above? Is it different than from part (c)?
g. Suppose you are instead doing a two-sided test: Given H0: ?=44.0, H1: ? <> 44.0 and ?=0.05. Calculate the test critical values and state the conclusion of the test for the sample mean above.
h. Supposed that, unknown to you, the distribution of X had shifted to ~NORM(42.8, 3.3). For n=30, calculate power and ? (type II error) for the two-sided hypothesis test of part (g).

[32pts] X NORM(44.0, 3.2). A sample mean of 43.7 is observed, for n=32. Given H0: ?=44.0, H1: ? < 44.0, and ?=0.05. This is a test on the mean for a single population.
a. What test statistic should be used? (Z, T, ?², F?)? Why?
b. What is the critical value of the test statistic to use for this test? What is the accept region (accept H0) and reject region (reject H0)?
c. Based on the critical value, what is your conclusion regarding this test given the sample mean above?
d. What impact would decreasing ? (say to 0.01) have on the critical value? On the test? What does ? control?
e. What is the one-sided p-value for the sample mean above?
f. Based on the p-value from part (e), what is your conclusion regarding this test given the sample mean above? Is it different than from part (c)?
g. Suppose you are instead doing a two-sided test: Given H0: ?=44.0, H1: ? <> 44.0 and ?=0.05. Calculate the test critical values and state the conclusion of the test for the sample mean above.
h. Supposed that, unknown to you, the distribution of X had shifted to NORM(42.8, 3.3). For n=30, calculate power and ? (type II error) for the two-sided hypothesis test of part (g).

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