386 Hypothesis Tests for a Mean 7.3 ACTIVITY APPLET You can find the interactive applet for this activity at MyLab Statistics. 386 CHAPTER 7 Hypothesis Testing with One Sample The Hypothesis tests for a mean applet generates simulations to investigate hypothesis tests for a mean. Specify the Sample size, the shape of the Distribution (Normal or Right skewed), the true population mean (Mean), the true population standard deviation (Std. dev.), the null value for the mean (Null mean), and the alternative for the test (Alternative). Click Update applet to load the applet with the specified parameters. Click 1 test, 5 tests, or 1000 tests to generate samples of the specified size with a proportion of successes equal to True p. For each sample, a hypothesis test based on the T@statistic is performed, and the T-statistic or the P-value (click one) for the test is plotted. Values colored in red represent tests where the null hypothesis is rejected at the specified level of significance. The default level of 0.05 can be changed by adjusting the Level. The table above the graph tracks the cumulative results and shows the Proportion of the hypothesis tests where the null hypothesis was rejected. Press Reset to clear existing results and start a new simulation. EXPLORE Step 1 Specify values for the Sample size, Mean, Std. dev., Null mean, and Alternative. Step 2 Click 1 test, 5 tests, or 1000 tests to generate hypothesis tests. DRAW CONCLUSIONS 1. Set Sample size = 15, Mean = 40, Std. dev. = 5, and the Distribution to “Normal.” Test the claim that the mean is equal to 40. What are the null and alternative hypotheses? Run the simulation for at least 1000 hypothesis tests. Compare the proportions of null hypothesis rejections at the 0.05 level and the 0.01 level. Is this what you would expect? Explain. 2. Suppose a null hypothesis is rejected at the 0.01 level. Will it be rejected at the 0.05 level? Explain. Suppose a null hypothesis is rejected at the 0.05 level. Will it be rejected at the 0.01 level? Explain. 3. Set Sample size = 25, Mean = 25, Std. dev. = 3, and the Distribution to “Normal.” Test the claim that the mean is at least 27. What are the null and alternative hypotheses? Run the simulation for at least 1000 hypothesis tests. Compare the proportions of null hypothesis rejections at the 0.05 level and the 0.01 level. Is this what you would expect? Explain. APPLET Test H : μ=50 vs. H : μ<50, Normal population (μ=50, б=10)Type=T 1 test Sample size 5 tests 1000 tests Update Applet Reset Info Sample size: Null mean: Mean: Alternative: 100 Distribution: Normal 100 < 50 50 Std. dev.: 10 0 A T-statistic -6 -4 0 150 4 2 0 -2 6 100 50 P-value Rolls Level 0.05 -1.66 1000 979 51 0.051 Frequency T-statistic Critical values Reject null Total Proportion 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000
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