Respuesta :
If the null hypothesis is correct, there is a 0.03 percent chance that the observed result (18%) or a more severe outcome will occur. The right response in this case is option D.
In this case, the percentage of the stated mortality rate is 23%, or [tex](p_{0} =0.23)[/tex]. Moreover, a fatality rate of less than 23% is asserted.
Alternative hypothesis:
[tex]H_{1}:p < p_{0}[/tex]
Null hypothesis :
[tex]H_{0} : p\geq p_{0}[/tex]
It will be a left-tail test since the alternative hypothesis is less than the specified value. If we were to use a 0.05 threshold of significance, the left tail test's p-value would be (0.03)0.05. This indicates that there is a 95% chance that the null hypothesis is false.
Complete question:
The death rate from a particular form of cancer is 23%. Researchers believe that a new, experimental drug will lower this death rate. They conduct an experiment and find that when treated with this experimental drug, only 15 out of 84 patients (18%) die during the initial year. After running a z of the proportion test statistic, the researchers find a p-value of .03. Which definition of a p-value is the most accurate?
A. The probability that the observed result (18%) or a result more extreme will occur if the null hypothesis is true is .03.
B. The probability that the alternative hypothesis (that the experimental drug will lower the death rate) is true is .03.
C. The probability that the observed result (18%) will happen again is .03.
D. The probability that the null hypothesis (that the experimental drug will not change the existing death rate of 23%) is true is .03.
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