Hypothesis Testing For a Population Mean
The Idea of Hypothesis Testing
Suppose we want to show that only children have an average higher cholesterol level than the national average. It is known that the mean cholesterol level for all Americans is 190. Construct the relevant hypothesis test: H0: = 190
H1: > 190
We test 100 only children and find that
x = 198
and suppose we know the population standard deviation
Do we have evidence to suggest that only children have an average higher cholesterol level than the national average? We have
z is called the test statistic.
Since z is so high, the probability that Ho is true is so small that we decide to reject H0 and accept H1. Therefore, we can conclude that only children have a higher average cholesterol level than the national average.
Suppose that = .05. We can draw the appropriate picture and find the z score for -.025 and .025. We call the outside regions the rejection regions.
We call the blue areas the rejection region since if the value of z falls in these regions, we can say that the null hypothesis is very unlikely so we can reject the null hypothesis Example
50 smokers were questioned about the number of hours they sleep each day. We want to test the hypothesis that the smokers need less sleep than the general public which needs an average of 7.7 hours of sleep. We follow the steps below.
Compute a rejection region for a significance level of .05. If the sample mean is 7.5 and the population standard deviation is 0.5, what can you conclude?
First, we write write down the null and alternative hypotheses H0: = 7.7 H1: < 7.7 This is a left tailed test. The z-score that corresponds to .05 is -1.645. The critical region is the area that lies to the left of -1.645. If the z-value is less than -1.645 there we will reject the null hypothesis and accept the...
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