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Comparing Two Means

Comparing Two Means. Two Sample t- tests and t -intervals. Example 1:.

callum-holman
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Comparing Two Means

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  1. Comparing Two Means Two Sample t-tests and t-intervals

  2. Example 1: Resting pulse rates for a random sample of 26 smokers had a mean of 80 beats per minute (bpm) and a standard deviation of 5 bpm. Among 32 randomly chosen nonsmokers, the mean and standard deviation were 74 and 6 bpm. Both sets of data were roughly symmetric and had no outliers. Is there evidence of a difference in mean pulse rate between smokers and non-smokers? How big?

  3. Hypothesis: There is no difference between the mean resting pulse rate for smokers and non-smokers. There is a difference between the mean resting pulse rate for smokers and non-smokers

  4. Conditions: • Randomization: Stated as random samples • Independence: The groups are independent of each other • Nearly Normal: Both sets of data were stated as roughly symmetric and unimodal All conditions have been met to use Student’s t-Model for a two-sample t-test.

  5. Mechanics:

  6. Conclusion: Since the P-Value is less than alpha (0.00011<0.05) we reject the null hypothesis. There is statistically significant evidence that there is a difference in the mean resting pulse rate of smokers and non-smokers.

  7. Confidence Interval: • Same Conditions We are 95% confident that the average resting pulse rate for smokers is between 3.1 and 8.9 beats per minute higher than for non-smokers.

  8. Example 2 • Here are the saturated fat content (in grams) for several pizzas sold by two national chains. Do the two pizza chains have significantly different mean saturated fat contents?

  9. Hypothesis: There is no difference in the mean saturated fat contents of the two pizza chains There is a difference in the mean saturated fat contents of the two pizza chains

  10. Conditions: • Randomization: Not stated as random, we will assume that the samples are representative of all pizzas for the two chains • Independence: The pizza chains are independent of each other • Nearly Normal: Normal probability plots of both graphs are approximately linear. All conditions have been met to use Student’s t-Model for a two-sample t-test.

  11. Mechanics:

  12. Conclusion: Since the P-Value is less than alpha (0.00003<0.05) we reject the null hypothesis. There is statistically significant evidence that there is a difference in the mean saturated fat content between the two pizza chains.

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