Test Statistic for Proportion: 31% of all traffic related deaths were alcohol-related

[Frosty]

Sup everyone, first post.

4) According to the CDC, 31% of all traffic related deaths were alcohol-related. A sheriff notices that, among the 44 traffic deaths in her county in the past 3 years, 21 were alcohol-related. She is worried that alcohol is a bigger problem in her county than in the nation.
Part A: Using the null hypothesis that traffic deaths in her county are 31% likely to be alcohol-related, she creates a sampling distribution with n=44, p=.31 and SE=0.070. What is the probability that 21 or more of the 44 fatalities are likely to be alcohol-related due to chance?
a) 0.32
b) 0.25
c) 0.05
d) 0.01

I know that you first find the z score by using formula

[FONT=MathJax_Math-italic]Z[FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math-italic]p[/FONT][FONT=MathJax_Main]ˆ[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math-italic]p[/FONT][FONT=MathJax_Main]0[/FONT][FONT=MathJax_Math-italic]p[/FONT][FONT=MathJax_Main]0[/FONT][FONT=MathJax_Main] [/FONT][FONT=MathJax_Math-italic]q[/FONT][FONT=MathJax_Main]0[/FONT][FONT=MathJax_Math-italic]n[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Size2]√[/FONT][/FONT]ddd​

I know the p hat is .477 and the SE or denominator is .070(duh). What I want to know is how to find the p0 or the hypothesized value?

Thanks in advance.

 

[Dr.Peterson]

Sup everyone, first post.

4) According to the CDC, 31% of all traffic related deaths were alcohol-related. A sheriff notices that, among the 44 traffic deaths in her county in the past 3 years, 21 were alcohol-related. She is worried that alcohol is a bigger problem in her county than in the nation.
Part A: Using the null hypothesis that traffic deaths in her county are 31% likely to be alcohol-related, she creates a sampling distribution with n=44, p=.31 and SE=0.070. What is the probability that 21 or more of the 44 fatalities are likely to be alcohol-related due to chance?
a) 0.32
b) 0.25
c) 0.05
d) 0.01

I know that you first find the z score by using formula z = (p^ - p₀)/sqrt(p₀ q₀ /n).

I know the p hat is .477 and the SE or denominator is .070(duh). What I want to know is how to find the p0 or the hypothesized value?

Thanks in advance.

The hypothesized value is the value that is hypothesized: that is, the value that is supposed for the sake of comparison.

The null hypothesis here would be that p equals the currently accepted value, 31%. The alternate hypothesis is what is being asked: is p actually greater than that?

So what you are calling p₀ is what they have called p in the problem statement.

Here is a typical explanation of the process. Note that they use the name p₀ as you did, and they define it as the value used in the null hypothesis. In their example, the null hypothesis is that the proportion is 0.5, so that is the p₀ they use.