Topic 10: Hypothesis Testing

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Topic 10: Hypothesis Testing Hypothesis testing for a single proportion Hypothesis testing for a single mean

Hypothesis Testing For a proportion

Hypothesis Testing Example A manufacturer claims that only 2% of the women using the company’s birth control pill suffer from side effects. Recent investigations by several journalists suggest this estimate is too low. We want to test the manufacturers claim. How would we do that?

Hypothesis Testing Example A manufacturer claims that only 2% of the women using the company’s birth control pill suffer from side effects. Recent investigations by several journalists suggest this estimate is too low. We want to test the manufacturers claim.

Calculator 1-PropZTest (proportions, hypothesis testing) p0: .02 x: 23 Select prop > p0 Select Calculate for P-value; Select Draw to see the normal curve and get the P-value

Assumptions for a hypothesis test for a population proportion We have a random sample from the population The sample is large enough so that we see at least 15 observations of both possible outcomes

Hypothesis Testing For a Mean

Hypothesis Testing Example In order to monitor the ecological health of the Florida Everglades, various measurements are recorded at different times. The bottom temperatures are recorded at the Garfield Bight station and the mean of 30.4 Celsius was obtained for 61 temperatures recorded on 61 different days, with a standard deviation of 1.7 Celsius. Test the claim that the population mean is 30 Celsius.

Calculator Ttest (mean, hypothesis testing) 0: 30 x: 30.4 Sx: 1.7  ≠ 0

Assumptions for a hypothesis test for a population mean We have a random sample from the population Either sample size is large (30 or larger) or the population is normally distributed

Make a Decision The P-value is a cutoff: if P-value < α we reject the null hypothesis; otherwise, we fail to reject the null hypothesis. We can also express our conclusion using the table below (ranges can vary depending on the application). Could we have made an error?

Could We Have Made an Error? Yes Sometimes one is more serious, sometimes the other!