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Psychologists know that human reaction times, in milliseconds, to light are normally distributed with mean 240 and standard deviation 45.
A baseball coach records the reaction time of his 65 players, and summarizes the data in the table below.
Write down the value of k.
The coach believes his players' reaction times do not follow the same distribution. He decides to perform a χ2 goodness of fit test at the 1% significance level.
State the null and alternative hypotheses for this test.
The critical value for this test is 11.34.
Using this critical value, determine the outcome of the coach's test.
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The number of defective widgets produced by a machine in a batch of 40 can be modeled by a binomial distribution. The manufacturer claims the defect rate is 5%. An inspector, Lee, believes the true defect rate is higher and decides to conduct a test:
He inspects one batch of 40 widgets.
If he finds 3 or more defectives, he will reject the manufacturer’s claim.
State a suitable null and alternative hypothesis for Lee’s test.
Find the probability of a Type I error.
Suppose the true defect rate is actually 8%.
Find the probability of a Type II error.
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A doctor claims that 20% of people in the United States are overweight. A university believes the true proportion to be much higher. They take a simple random sample of 100 Americans and find that 31 of them are overweight. The university team decides to conduct a z-test for proportion on the data with significance level 5%.
State the null and alternative hypotheses for this test.
Find the p-value for this test.
State the outcome of the test.
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