Suppose that you are testing the hypotheses Ho. p-0.21 vs HA p#0.21. A sample of

Question

Suppose that you are testing the hypotheses Ho. p-0.21 vs HA p#0.21. A sample of sze 150 results in a sample proportion of 0.25. a) Construct a 90% confidence interval for p. b) Based on the confidence interval, can you reject o at a 0.10 Explain. c) What is the difference between the standard error and standard deviation of the sample proportion? d) Which is used in computing the confidence interval? a) The 90% confidence interval for p is (DD). Round to three decimal places as needed.) b) Determine the conclusion for the hypothesis test based on the confidence interval. Since the confidence interval c) What is the difference between the standard error and standard deviation of the sample proportion? contain the null hypothesis value, it indicates to Vthe null hypothesis at a 0.10 OA The standard error is based on the sample proportion, D while the standard deviation is based on the hypothesized proportion, po OB. The standard error is based on the sample proportion, Po while the standard deviation is based on the hypothesized proportion, p OC. The standard error is based on the hypothesized proportion, po, while the standard deviation is based on the sample proportion, D D. The standard error is based on the hypothesized proportion, p, while the standard deviation is based on the sample proportion, po d) Which value is used in computing the confidence interval, the standard error of the sample proportion or the standard deviation of the sample proportion? O the standard deviation O the standard error

Explanation / Answer

a)
CI for 90%
n = 150
p = 0.25
z-value of 90% CI = 1.6449
SE = sqrt(p*(1-p)/n)
= sqrt(0.25*0.75/150)
= 0.03536

ME = z*SE
= 1.6449*0.03536
= 0.05815

Lower Limit = p - ME = 0.25 - 0.05815 = 0.19185
Upper Limit = p + ME = 0.25 - 0.05815 = 0.30815
90% CI (0.192 , 0.308)

b)
Since the CI contains the null hypothesis value, it indicates to fail to reject the null hypothesis

c)
Option A

d)
the standard error

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