Question 1183081
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Part (a)


I think you meant to say "null and alternative hypothesis". I'm not familiar with the term "void" when it comes to statistical hypotheses.



The null would be p = 0.40 which is based on previous studies.


The alternative hypothesis is p < 0.40


We can use this shorthand notation
H0: p = 0.40
H1: p < 0.40
to represent the null and alternative hypothesis


Based on the inequality sign of the alternative hypothesis, we have a left tailed test.


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Part (b)


x = number of successes 
x = number of people confident in reaching their goals
x = 31


n = sample size
n = number of people asked in the survey
n = 700


phat = sample proportion
This value is pronounced as "p-hat" though I'll leave out the minus sign to avoid confusion later on.


phat = x/n 
phat = 31/700 
phat = 0.0442857 approximately


SE = standard error
SE = sqrt(p*(1-p)/n)
SE = sqrt(0.40*(1-0.40)/700)
SE = 0.0185164 also approximate


We have enough to compute the z test statistic
z = (phat - p)/SE
z = (0.0442857 - 0.40)/0.0185164
z = -19.210769912078


The test statistic is approximately -19.211


As you'll see in the next part, this isn't good. 

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Part (c)


Because the test statistic is very far away from the interval -3 < z < 3, this means that the p-value is effectively zero.


In other words, P(Z < -19.211) = 0
It's technically not exactly equal to 0, but it's so very very small that it might as well be treated as zero.


I'm not sure if your teacher intended this. There might be a typo and that would mean the result of part (b) should be something else. Ideally we want a z value somewhere between z = -3 and z = 3. 


If I had to guess, it's possible that the "700" should be "70". Or perhaps the "31" should be much larger. I would ask your teacher for clarification.
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