Comparing Two Independent Population Proportions Quiz

PDF page 556: population from being over-sampled and causing incorrect results. Comparing two proportions, like comparing two means, is common. If two estimated proportions are different, it may be due to a difference in the populations or it may be due to chance. A hypothesis test can help determine if a difference in the estimated proportions reflects a difference in the population proportions. The difference of two proportions follows an approximate normal distribution. Generally, the null hypothesis states that the two proportions are the same. That is, H0: pA = pB. To conduct the test, we use a pooled proportion, pc. The pooled proportion is calculated as follows:

PDF page 556: population from being over-sampled and causing incorrect results. Comparing two proportions, like comparing two means, is common. If two estimated proportions are different, it may be due to a difference in the populations or it may be due to chance. A hypothesis test can help determine if a difference in the estimated proportions reflects a difference in the population proportions. The difference of two proportions follows an approximate normal distribution. Generally, the null hypothesis states that the two proportions are the same. That is, H0: pA = pB. To conduct the test, we use a pooled proportion, pc. The pooled proportion is calculated as follows:

PDF page 556: population from being over-sampled and causing incorrect results. Comparing two proportions, like comparing two means, is common. If two estimated proportions are different, it may be due to a difference in the populations or it may be due to chance. A hypothesis test can help determine if a difference in the estimated proportions reflects a difference in the population proportions. The difference of two proportions follows an approximate normal distribution. Generally, the null hypothesis states that the two proportions are the same. That is, H0: pA = pB. To conduct the test, we use a pooled proportion, pc. The pooled proportion is calculated as follows:

PDF page 556: Problem Two types of medication for hives are being tested to determine if there is a difference in the proportions of adult patient reactions. Twenty out of a random sample of 200 adults given Medication A still had hives 30 minutes after taking the medication. Twelve out of another random sample of 200 adults given Medication B still had hives 30 minutes after taking the medication. Test at a 1 percent level of significance.

PDF page 557: P′A – P′B = difference in the proportions of adult patients who did not react after 30 minutes to Medication A and to Medication B. H0: pA = pB pA – pB = 0 Ha: pA ≠ pB pA – pB ≠ 0 The words is a difference tell you the test is two-tailed. Distribution for the test: Since this is a test of two binomial population proportions, the distribution is normal:

PDF page 557: P′A – P′B follows an approximate normal distribution. Calculate the p-value using the normal distribution: p-value = 0.1404.

PDF page 557: P′A – P′B = 0.1 – 0.06 = 0.04.

PDF page 557: Compare α and the p-value: α = 0.01 and the p-value = 0.1404. α < p-value.

PDF page 557: Make a decision: Since α < p-value, do not reject H0. Conclusion: At a 1 percent level of significance, from the sample data, there is not sufficient evidence to conclude that there is a difference in the proportions of adult patients who did not react after 30 minutes to Medication A and Medication B.

PDF page 558: Ha: pF < pM Ha: pF – pM < 0 The words less than tell you the test is left-tailed. Distribution for the test: Since this is a test of two population proportions, the distribution is normal:

PDF page 559: p-value = 0.1045 Estimated proportion for females: 0.0719 Estimated proportion for males: 0.082

PDF page 559: press ENTER. The p-value is p = 0.1045 and the test statistic is z = –1.256.

PDF page 559: Ha: pW > pA Ha: pW – pA > 0 The words more popular indicate that the test is right-tailed. Distribution for the test: The distribution is approximately normal.