Hypothesis Tests One Sample Means

Steps: Assumptions Hypothesis statements & define parameters Calculations Conclusion, in context

Assumptions for z-test (t-test): YEA – These are the same assumptions as confidence intervals!! Have an SRS of context Distribution is (approximately) normal Given Large sample size Graph data s is known (unknown)

Writing Hypothesis statements: Null hypothesis – is the statement being tested; this is a statement of “no effect” or “no difference” Alternative hypothesis – is the statement that we suspect is true H0: m = 4 Ha: m < 4

The form: Null hypothesis H0: parameter = hypothesized value Alternative hypothesis Ha: parameter > hypothesized value Ha: parameter < hypothesized value Ha: parameter = hypothesized value

Example 5: Drinking water is considered unsafe if the mean concentration of lead is greater than 15 ppb (parts per billion). Suppose a community randomly selects of 25 water samples and computes a t-test statistic of 2.1. Assume that lead concentrations are normally distributed. Write the hypotheses, calculate the p-value & write the appropriate conclusion for a = 0.05. H0: m = 15 Ha: m > 15 Where m is the true mean concentration of lead in drinking water P-value = tcdf(2.1,10^99,24) =.0232 t=2.1 Since the p-value < a, I reject H0. There is sufficient evidence to suggest that the mean concentration of lead in drinking water is greater than 15 ppb.

Example 8: The Degree of Reading Power (DRP) is a test of the reading ability of children. Here are DRP scores for a random sample of 44 third-grade students in a suburban district: (data on note page) At the a = .1, is there sufficient evidence to suggest that this district’s third graders reading ability is different than the national mean of 34?

I have an SRS of third-graders Normal? How do you know? Since the sample size is large, the sampling distribution is approximately normally distributed OR Since the histogram is unimodal with no outliers, the sampling distribution is approximately normally distributed Do you know s? What are your hypothesis statements? Is there a key word? s is unknown H0: m = 34 where m is the true mean reading Ha: m = 34 ability of the district’s third-graders Plug values into formula. p-value = tcdf(.6467,1E99,43)=.2606(2)=.5212 Use tcdf to calculate p-value. a = .1

Compare your p-value to a & make decision Conclusion: Since p-value > a, I fail to reject the null hypothesis. There is not sufficient evidence to suggest that the true mean reading ability of the district’s third-graders is different than the national mean of 34. Write conclusion in context in terms of Ha.