We have an SRS of size ten from a Normal population with standard deviation ?=1σ=1 , and we will do a test at level α=0.05α=0.05 . At the bottom of the screen, a button allows you to choose a value of the mean ?μ and then to generate samples from a population with that mean. (a) Set ?=0μ=0 , so that the null hypothesis is true. Each time you click the button, a new sample appears. If the sample ?¯x¯ lands in the colored region, that sample rejects ?0H0 at the 5%5% level. Click 100100 times rapidly, keeping track of how many samples reject ?0H0 . Use your results to estimate the probability of a Type I error. If you kept clicking forever, what probability wou
Go to the Statistical Significance applet. This applet carries out tests at a fixed significance level. When you arrive, the applet is set for a test with the hypotheses of:
?0:?=0H0:μ=0
??:?>0Ha:μ>0
We have an SRS of size ten from a Normal population with standard deviation ?=1σ=1 , and we will do a test at level α=0.05α=0.05 . At the bottom of the screen, a button allows you to choose a value of the mean ?μ and then to generate samples from a population with that mean.
(a) Set ?=0μ=0 , so that the null hypothesis is true. Each time you click the button, a new sample appears. If the sample ?¯x¯ lands in the colored region, that sample rejects ?0H0 at the 5%5% level. Click 100100 times rapidly, keeping track of how many samples reject ?0H0 . Use your results to estimate the probability of a Type I error.
If you kept clicking forever, what probability would you get? (Enter your answer rounded to two decimal places.)
probability of Type I error:
(b) Now set ?=0.8μ=0.8 . This test has power 0.8120.812 against this alternative. Click 100100 times rapidly, keeping track of how many samples fail to reject ?0H0 . Use your results to estimate the probability of a Type II error. If you kept clicking forever, what probability would you get? (Enter your answer rounded to three decimal places.)
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