Suppose that you are testing the hypotheses Ho: p= 0.22 vs. HA: p> 0.22. A sampl

Question

Suppose that you are testing the hypotheses Ho: p= 0.22 vs. HA: p> 0.22. A sample of size 200 results in a sample proportion of 0.26. a) Construct a 90% confidence interval for p. b) Based on the confidence interval, can you reject Ho at = 0.05? 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 (Round to three decimal places as needed.) b) Determine the conclusion for the hypothesis test based on the confidence interval Since the confidence interval | contain the null hypothesis value the null hypothesis at = 0.05. c) What is the difference between the standard error and standard deviation of the sample proportion? A. O B. O C. The standard error is based on the sample proportion, P, while the standard deviation is based on the hypothesized proportion, p. The standard error is based on the sample proportion, p, while the standard deviation is based on the hypothesized proportion, po The standard error is based on the hypothesized proportion, Po. while the standard deviation is based on the sample proportion, p. The standard error is based on the hypothesized proportion, p, while the standard deviation is based on the sample proportion, Po D. 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 error O the standard deviation

Explanation / Answer

Solution:-

a) Tcritiical = +1.667

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 119
Alternative hypothesis: 119

n = 71

D.F = 71 - 1

D.F = 70, alpha = 0.05

Tcritiical = +1.667

b) zcritical = 2.33

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P < 0.09
Alternative hypothesis: P > 0.09

Note that these hypotheses constitute a one-tailed test.

zcritical = 2.33

c) zcritical = +1.645

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.60
Alternative hypothesis: P 0.60

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.

zcritical = +1.645

d) zcritical = - 1.275

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P > 0.04
Alternative hypothesis: P > 0.04

Note that these hypotheses constitute a one-tailed test.

zcritical = -1.275

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