SOLUTION: Consider the following hypotheses: H0: p ≥ 0.47 HA: p < 0.47 Compute the p-value based on the following sample information. (You may find it useful to reference the appropr

Question 1163241: Consider the following hypotheses:
H0: p ≥ 0.47
HA: p < 0.47
Compute the p-value based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table) (Round "z" value to 2 decimal places. Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)
p¯ = 0.38; n = 430
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the null assumption is that the population ratio is greater than .47
the alternate assumption is that the population ratio is less than .47
you are given that the sample ratio is .38 and that the number of elements in the sample is 430.
you first need to find the population standard deviation.
that is given by the equation of:
s = sqrt(p * q / n)
p is the population ratio.
q is equal to 1 minus the population ratio
n is the sample size.
you get:
p = .47
q = .53
n = 430
calculate s to get:
s = sqrt(.47 * .53 / 430) = .0240687001
since you are told to round this to at least 4 decimal places, rounding to 5 decimal places is a pretty good place to stop.
you get:
s = .02407.
you then want to calculate the z-score.
the formula for z-score is z = (x - m) / s
z is the x-score
x is the raw score (.38 in this case)
m is the mean (.47 in this case)
s is the standard error (.02407 in this case)
the formula becomes:
z = (.38 - .47) / .02407 = -3.739094308.
round this to -3.74
this is a very low z-score.
my calculator says that the probability of getting a z-score less than this is equal to .00009204803911.
rounding this to 5 decimal places makes it .00009
round this to 4 decimal places makes it .0001
i checked the z-score tables and they tell me that the probability of getting a z-score less than that is the same when rounded to 5 decimal places.
therefore, your answer should be that that the p-value is .0001
that's a very low p-value which means that the probability of getting a sample of 430 elements to have a population of .38 or less is negligible and that you can assume that the population ratio is less than .47 with a high degree of probability of being correct.
that's my take on the solution to this problem.
your solution is that the p-value is .0001, as far as i can tell based on my understanding of what they're asking you to find.

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