Question

19.10 A number of investigators have reported a tendency for more people to die (from natural causes, such as cancer and strokes) after, rather than before, a major holiday. This post-holiday death peak has been attributed to a number of factors, including the willful postponement of death until after the holiday, as well as holiday stress and post-holiday depression. Writing in the Journal of the American Medical Association (April 11, 1990), Phillips and Smith report that among a total of 103 elderly California women of Chinese descent who died of natural causes within one week of the Harvest Moon Festival, only 33 died the week before, while 70 died the week after.

(a) Using the .05 level of significance, test the null hypothesis that, in the under lying population, people are equally likely to die either the week before or the week after this holiday.

(b) Specify the approximate p-value for this test result.

(c) How might this result be reported in the literature?

please help ,show work.

Answer 1

1)
Null hypothesis, people are equally likely to die either the week before or the week after this holiday. p = 50%
An alternative hypothesis, people are NOT equally likely to die either the week before or the week after this holiday. p =/= 50%

X=   33  
n=   70  
p-hat = X/n = 0.4714 = 33/70
po=   0.500

test statistic, z = (phat-p)/sqrt(p*(1-p)/n)
=(0.4714-0.5)/SQRT(0.5*(1-0.5)/70)
-0.479

z(a/2)
z(0.05/2)
1.960

With |z| < z(a/2), i fail to reject the null hypothesis and conclude that people are equally likely to die either the week before or the week after this holiday. p = 50%

2)
p-value
2*(1-P(z<|z|)
2*(1-P(z<abs(-0.47857))
normsdist(abs(-0.47857))
0.6322

3)
With z=-0.479, p>5%, i fail to reject the null hypothesis at 5% level of significance and conclude that people are equally likely to die either the week before or the week after this holiday.
there is no sufficient evidence to support the claim that people are NOT equally likely to die either the week before or the week after this holiday. p =/= 50%