Question 259817: Can you please help with this statistics problem?
During the period 1990-1998 there were 46 Atlantic hurricanes, of which 19 struck the United States. During the period 1999-2006 there were 70 hurricanes, of which 45 struck the United States.
a) What is the appropriate null and alternate hypothesis to determine if the
proportion of hurricanes striking the United States increased?
b) Using α = 0.01, what is the critical value for the hypothesis test?
c) What is the test statistic for the hypothesis test?
d) Draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.
e) What is the p-value for the hypothesis test?
Thank you!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! During the period 1990-1998 there were 46 Atlantic hurricanes, of which 19 struck the United States. During the period 1999-2006 there were 70 hurricanes, of which 45 struck the United States.
a) What is the appropriate null and alternate hypothesis to determine if the
proportion of hurricanes striking the United States increased?
Ho: p(new)-p(old)= 0
Ha: p(new)-p(old)< 0
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b) Using α = 0.01, what is the critical value for the hypothesis test?
invNorm(0.01) = -2.3263
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c) What is the test statistic for the hypothesis test?
z((19/46)-(45/70)) = (0.41-0.64)/sqrt(0.64*0.36/70 + 0.41*0.59/46)
= -2.4874
d) Draw a conclusion for the hypothesis test.
Since the ts is in the rejection interval below the cv, reject Ho.
The proportion of hurricanes that hit the US has changed, according
to these test results.
Make sure you state your conclusion in the context of the problem.
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e) What is the p-value for the hypothesis test?
p-value = P(z< ts) = P(z< -2.4874) = normalcdf(-100,-2.4874) = 0.0064..
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Cheers,
Stan H.
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