ficance level to 5%, should she reject her hypothesis? (a) What is Alice’s null hypothesis? What should she set μ0 equal to for the sake of calculations? (b) Alice’s test is a sample of 25 runners. If her hypothesis is true, what is the mean and standard deviation of the sampling distribution? Remember, Alice is hypothesizing about a mean. (c) Since this is a mean, should we use the normal table or the t-distribution table?
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Alice takes as her hypothesis that the average time it takes to run a mile is 8.12 minutes. In a recentevent, 25 people ran a mile with an average time of 8.8 minutes and a standard deviation of 1.1 minutes.If Alice sets her significance level to 5%, should she reject her hypothesis?
(a) What is Alice’s null hypothesis? What should she set μ0 equal to for the sake of calculations?
(b) Alice’s test is a sample of 25 runners. If her hypothesis is true, what is the mean and standard deviation of the sampling distribution? Remember, Alice is hypothesizing about a mean.
(c) Since this is a mean, should we use the normal table or the t-distribution table?
(d) Which type of sample mean would cause Alice to reject her null? A mean larger than her hypothesis (right-tailed), a mean less than her hypothesis (left-tailed), or either? (two-tailed)
(e) Alice will only rethink her position if something happens with less than 5% probability. What T-score will a sample have to achieve? Use the table, choosing a value for degrees of freedom on the left and a significance upstairs. Remember, the table gives you probability ON THE RIGHT.
(f) The distribution from (b) and (c) is Alice’s model of the world. However, Alice to an actual sample from the real world. What was the sample mean x?
(g) What is the t-score of x? In other words, what is the value of the test statistic?
(h) Is this test statistic large or small enough to cause Alice to reject her null hypothesis?
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