1. Height and Weight Presented by Clarence Cheng & Kehinde Opere

2. Hypotheses – Height (z- and t-tests) Lower 1–tail test Lower 1–tail test –Null hypothesis H o : the average height for 2004 SCSU SDP students is not significantly different from 169 cm –Alternative hypothesis H a : the average height is less than 169 cm Or… –H 0 : μ h = 169 cm –H a : μ h < 169 cm Upper 1–tail test Upper 1–tail test –Null hypothesis H o : see above –Alternative hypothesis H a : the average height is greater than 169 cm Or… –H 0 : μ h = 169 cm –H a : μ h > 169 cm

3. Hypotheses – Height cont. (z- and t-tests) 2–tail test 2–tail test –Null hypothesis H 0 : see above –Alternative hypothesis H a : the average height is not 169 cm Or… –H 0 : μ h = 169 cm –H a : μ h 169 cm α =.05, or 5% (this will apply to all following slides) α =.05, or 5% (this will apply to all following slides)

4. Testing… (z) 1-Tail: 1-Tail: –z α = 1.645 for upper 1-tail test and -1.645 for lower 1- tail test –z = (x bar – μ)/(s/n).2093 –Because -1.645 <.2093 < 1.645, H 0 can be accepted as true for both the upper and lower 1-tailed z tests. –In other words, with a 5% chance of committing a Type I error, the average height of 2004 SCSU SDP students is not significantly different from 169 cm. –To avoid repetition, the preceding conclusion will not be printed on other slides in this presentation with the title Testing…

5. Testing… (z) 2-Tail: 2-Tail: –z α = 1.96 for 2-tail test –z = (x bar – μ)/(s/n).2093 –Because -1.96 <.2093 < 1.96, H 0 can be accepted as true for the 2-tailed z test.

6. Testing… (t) 1-Tail: 1-Tail: –t α = 1.782 for upper 1-tail test and -1.782 for lower 1-tail test –t = (x bar – μ)/(s/n).2093 –Because -1.782 <.2093 < 1.782, H 0 can be accepted as true for both the upper and lower 1-tailed t tests.

7. Testing… (t) 2-Tail: 2-Tail: –t α = 2.179 for 2-tail test –t = (x bar – μ)/(s/n).2093 –Because -2.179 <.2093 < 2.179, H 0 can be accepted as true for the 2-tailed t test.

8. Descriptive Statistics – Height Mean: 169.4615 Median: 170 Mode: 170 Range: 30 Standard Deviation: 7.9516

9. Hypotheses – Weight (z- and t-tests) Lower 1–tail test Lower 1–tail test Null hypothesis H 0 : the average weight (in kg) for 2004 SCSU SDP students is not significantly different from 72 kg Null hypothesis H 0 : the average weight (in kg) for 2004 SCSU SDP students is not significantly different from 72 kg Alternative hypothesis H a : the average weight is less than 72 kg Alternative hypothesis H a : the average weight is less than 72 kgOr… H 0 : μ w = 72 kg H 0 : μ w = 72 kg H a : μ w < 72 kg H a : μ w < 72 kg Upper 1–tail test Upper 1–tail test Null hypothesis H 0 : see above Null hypothesis H 0 : see above Alternative hypothesis H a : the average weight is more than 72 kg Alternative hypothesis H a : the average weight is more than 72 kgOr… H 0 : μ w = 72 kg H 0 : μ w = 72 kg H a : μ w > 72 kg H a : μ w > 72 kg

10. Hypotheses – Weight cont. (z- and t-tests) 2-tail test 2-tail test Null hypothesis H 0 : see above Null hypothesis H 0 : see above Alternative hypothesis H a : the average weight is not 72 kg Alternative hypothesis H a : the average weight is not 72 kgOr… H 0 : μ w = 72 kg H 0 : μ w = 72 kg H a : μ w 72 kg H a : μ w 72 kg

11. Testing Again… (z) 1-Tail: 1-Tail: z α = 1.645 for upper 1-tail test and -1.645 for lower 1- tail test z α = 1.645 for upper 1-tail test and -1.645 for lower 1- tail test z = (x bar – μ)/(s/n) -.7736 z = (x bar – μ)/(s/n) -.7736 Because -1.645 < -.7736 < 1.645, H 0 can be accepted as true for both the upper and lower 1-tailed z tests. Because -1.645 < -.7736 < 1.645, H 0 can be accepted as true for both the upper and lower 1-tailed z tests. In other words, with a 5% chance of committing a Type I error, the average weight of 2004 SCSU SDP students is not significantly different from 72 kg. In other words, with a 5% chance of committing a Type I error, the average weight of 2004 SCSU SDP students is not significantly different from 72 kg. To avoid repetition, the preceding conclusion will not be printed on other slides in this presentation with the title Testing Again… To avoid repetition, the preceding conclusion will not be printed on other slides in this presentation with the title Testing Again…

12. Testing Again… (z) 2-Tail: 2-Tail: z α = 1.96 for 2-tail test z α = 1.96 for 2-tail test z = (x bar – μ)/(s/n).2093 z = (x bar – μ)/(s/n).2093 Because -1.96 <.2093 < 1.96, H 0 can be accepted as true for the 2-tailed z test. Because -1.96 <.2093 < 1.96, H 0 can be accepted as true for the 2-tailed z test.

13. Testing Again… (t) 1-Tail: 1-Tail: t α = 1.782 for upper 1-tail test and -1.782 for lower 1-tail test t α = 1.782 for upper 1-tail test and -1.782 for lower 1-tail test t = (x bar – μ)/(s/n) -.7736 t = (x bar – μ)/(s/n) -.7736 Because -1.782 < -.7736 < 1.782, H 0 can be accepted as true for both the upper and lower 1- tailed t tests. Because -1.782 < -.7736 < 1.782, H 0 can be accepted as true for both the upper and lower 1- tailed t tests.

14. Testing Again… (t) 2-Tail: 2-Tail: t α = 2.179 for 2-tail test t α = 2.179 for 2-tail test t = (x bar – μ)/(s/n) -.7736 t = (x bar – μ)/(s/n) -.7736 Because -2.179 < -.7736 < 2.179, H 0 can be accepted as true for the 2-tailed t test. Because -2.179 < -.7736 < 2.179, H 0 can be accepted as true for the 2-tailed t test.

15. Descriptive Statistics – Weight Mean: 69.0546 Median: 65.4 Mode: N/A Range: 36.82 Standard Deviation: 13.7280

16. A Graph Height vs. Weight – Scatterplot

17. Another Graph Height vs. Weight – Line Graphs

18. So, What Did That Mean? (the graphs) The scatterplot shows there is basically no correlation between height and weight. The points are for the most part evenly spread. Thus, height and weight are likely not related. The line graphs are further support for this notion, as the graphs tend to increase and decrease both simultaneously and inversely, showing they are independent of each other. The correlation coefficient for the two data sets is.0459 – this demonstrates the little correlation between height and weight as well.

19. Note… Calculations of means, medians, modes, ranges, standard deviations, and z and t values and the making of the graphs were done in Microsoft Excel.