Tutorial Exercise A random sample of 20 binomial trials resulted in 9 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05. (a) Can a normal distribution be used for the p distribution? Explain. (b) State the hypotheses. (c) Compute p and the corresponding standardized sample test statistic. (d) Find the P-value of the test statistic. (e) Do you reject or fail to reject H,? Explain. (f) What do the results tell you? Step 1 (a) Can a normal distribution be used for the p distribution? Explain. Recall that to test a proportion, p, assuming all requirements are met, the z values will be calculated using the following formula, where r is the number of successes, n is the number of trials, p = is the sample statistic, p is the population probability of success, and q = 1 - p represents the population probability of failure. p - p Z = pq In order to use the normal distribution to estimate the ôp distribution, the number of trials n should be sufficiently large so that both np > 5 and ng > 5. We will first check that these requirements are met. We have a random sample of 20 binomial trials resulting in 9 successes and we wish to test the claim that the population proportion of successes does not equal 0.50 using a significance level of 0.05. Therefore, we can define n, p, and q as follows. n = 20 p = 9
Tutorial Exercise A random sample of 20 binomial trials resulted in 9 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05. (a) Can a normal distribution be used for the p distribution? Explain. (b) State the hypotheses. (c) Compute p and the corresponding standardized sample test statistic. (d) Find the P-value of the test statistic. (e) Do you reject or fail to reject H,? Explain. (f) What do the results tell you? Step 1 (a) Can a normal distribution be used for the p distribution? Explain. Recall that to test a proportion, p, assuming all requirements are met, the z values will be calculated using the following formula, where r is the number of successes, n is the number of trials, p = is the sample statistic, p is the population probability of success, and q = 1 - p represents the population probability of failure. p - p Z = pq In order to use the normal distribution to estimate the ôp distribution, the number of trials n should be sufficiently large so that both np > 5 and ng > 5. We will first check that these requirements are met. We have a random sample of 20 binomial trials resulting in 9 successes and we wish to test the claim that the population proportion of successes does not equal 0.50 using a significance level of 0.05. Therefore, we can define n, p, and q as follows. n = 20 p = 9
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Problem 1P
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Transcribed Image Text:Tutorial Exercise
A random sample of 20 binomial trials resulted in 9 successes. Test the claim that the population proportion of successes does not
equal 0.50. Use a level of significance of 0.05.
(a) Can a normal distribution be used for the p distribution? Explain.
(b) State the hypotheses.
(c) Compute p and the corresponding standardized sample test statistic.
(d) Find the P-value of the test statistic.
(e) Do you reject or fail to reject H,? Explain.
(f) What do the results tell you?
Step 1
(a) Can a normal distribution be used for the ôp distribution? Explain.
Recall that to test a proportion, p, assuming all requirements are met, the z values will be calculated using the following formula,
where r is the number of successes, n is the number of trials, p =
is the sample statistic, p is the population probability of
success, and q = 1 – p represents the population probability of failure.
р — р
z =
pq
In order to use the normal distribution to estimate the p distribution, the number of trials n should be sufficiently large so that
both np > 5 and nq > 5. We will first check that these requirements are met.
We have a random sample of 20 binomial trials resulting in 9 successes and we wish to test the claim that the population
proportion of successes does not equal 0.50 using a significance level of 0.05. Therefore, we can define n, p, and q as follows.
n =
20
p =
9.
q = 1 - p = 19
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