document.write( "Question 1163241: Consider the following hypotheses:
\n" ); document.write( "H0: p ≥ 0.47
\n" ); document.write( "HA: p < 0.47
\n" ); document.write( "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.)
\n" ); document.write( "p¯ = 0.38; n = 430 \n" ); document.write( "
Algebra.Com's Answer #787274 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
the null assumption is that the population ratio is greater than .47
\n" ); document.write( "the alternate assumption is that the population ratio is less than .47
\n" ); document.write( "you are given that the sample ratio is .38 and that the number of elements in the sample is 430.
\n" ); document.write( "you first need to find the population standard deviation.
\n" ); document.write( "that is given by the equation of:
\n" ); document.write( "s = sqrt(p * q / n)
\n" ); document.write( "p is the population ratio.
\n" ); document.write( "q is equal to 1 minus the population ratio
\n" ); document.write( "n is the sample size.
\n" ); document.write( "you get:
\n" ); document.write( "p = .47
\n" ); document.write( "q = .53
\n" ); document.write( "n = 430
\n" ); document.write( "calculate s to get:
\n" ); document.write( "s = sqrt(.47 * .53 / 430) = .0240687001
\n" ); document.write( "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.
\n" ); document.write( "you get:
\n" ); document.write( "s = .02407.
\n" ); document.write( "you then want to calculate the z-score.
\n" ); document.write( "the formula for z-score is z = (x - m) / s
\n" ); document.write( "z is the x-score
\n" ); document.write( "x is the raw score (.38 in this case)
\n" ); document.write( "m is the mean (.47 in this case)
\n" ); document.write( "s is the standard error (.02407 in this case)
\n" ); document.write( "the formula becomes:
\n" ); document.write( "z = (.38 - .47) / .02407 = -3.739094308.
\n" ); document.write( "round this to -3.74
\n" ); document.write( "this is a very low z-score.
\n" ); document.write( "my calculator says that the probability of getting a z-score less than this is equal to .00009204803911.
\n" ); document.write( "rounding this to 5 decimal places makes it .00009
\n" ); document.write( "round this to 4 decimal places makes it .0001
\n" ); document.write( "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.
\n" ); document.write( "therefore, your answer should be that that the p-value is .0001
\n" ); document.write( "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.
\n" ); document.write( "that's my take on the solution to this problem.
\n" ); document.write( "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.\r
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