Hypothesis Tests for a Single Population Proportion

Full Answer Section

c. The critical value is:

zα = -1.645

d. The correct decision is to fail to reject the null hypothesis. e. The correct summary would be: There is not enough evidence to support the claim that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.33. 2. The null and alternative hypothesis are:

H0: p = 0.2
H1: p < 0.2

The test is left-tailed. Based on a sample of 500 people, 16% owned cats. The test statistic is:

z = (16 - 500 * 0.2) / √(500 * 0.2 * 0.8) = -2.58

The p-value is:

p = 0.005

Based on this, we reject the null hypothesis. 3. The null and alternative hypothesis are:

H0: p = 0.2
H1: p < 0.2

The test is left-tailed. Based on a sample of 700 people, 18% of them said they are confident of meeting their goals. The test statistic is:

z = (18 - 700 * 0.2) / √(700 * 0.2 * 0.8) = -1.73

The p-value is:

p = 0.082

Based on this, we fail to reject the null hypothesis. 4. The null and alternative hypothesis are:

H0: p = 0.2
H1: p > 0.2

The test is right-tailed. Based on a sample of 800 people, 23% owned cats. The test statistic is:

z = (23 - 800 * 0.2) / √(800 * 0.2 * 0.8) = 2.31

The p-value is:

p = 0.019

Based on this, we reject the null hypothesis. I hope this helps! Let me know if you have any other questions.

Sample Solution

a. The correct hypotheses are:

H0: p = 0.33
H1: p < 0.33

b. The test statistic is:

z = (205 - 761 * 0.33) / √(761 * 0.33 * 0.67) = -1.40

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