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10.30
A. hypotheses.
Ho: p (red) – p (yellow) > 0
Ha: p (red) – p (yellow) is not greater than 0

B. 1st Decision
One tail w/ alpha =1% Critical value is z = 2.326

C. Sample proportions and z statistic.
p – hat (red) = 20/153,348 ; p – hat (yellow) = 4/135,035
For Pooling: p – barber = (20+4) / (153348+135035) = 0.00002.08       z = [(20/153,348) - (4/135,035)] / sqrt [(0.00002.08)(0.999979) / 153348 + (0.00002.08)*0.999979/135035)] = 2.960988...

D. 2nd Decision
Seeing as test statistic is more than critical value, reject Ho

E. p - value and interpret it.
p - value = P(2.960988 < z < 10) = 0.00153
0.1533% chance that the test has stronger evidence against Ho.

F. If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why?
Yes it is statistically significant; yellow paint has reduced accidents.

G. Is the normality assumption fulfilled? Explain.
Yes: p1n1 > 5, q1n1 > 5 ; p2n2 > 5, p2n2 > 5

10.44
A. Hypotheses.
Ho: p(inactive) - P(active) = 0
Ha: p(inactive) - p(active) > 0

p-hat(inactive) = 97 / 2081 = 0.0466
p-hat(active) = 57 / 2325 = 0.0245
Pool the data you get p - bar = (97 + 57) / (2081 + 2325) = 0.0350
and q - bar = 1 – p - bar = 0.9650
alpha = 1%, critical value z = 2.326

B. Test statistic and p-value.
z(0.0466 - 0.0245) = 0.0221 / sqrt [(0.035 * 0.965 / 2081) + (0.035 * 0.965 / 2325)]
3.9849, p-value - 0.0000338

Interpret the results at alpha = .01
Where the p-value is less than alpha you should reject Ho; there is significant evidence that the use of this medicine reduces the number of deaths.

C. Is normality assured?
2081 * 0.035 = 72.84 > 5 and 2081 * 0.965 > 5
2325 * 0.035 = 70.86 > 5 and 2325 * 0.965 > 5

D. Is the difference large enough to be important?
p-value has strong evidence that Ha is true.

E. What else would medical researchers need to know before prescribing this drug widely? It could be the difference in family history and...

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