Confidence Intervals for Two Proportions

• Neither random condition nor Large Count condition is met

• The Random condition is met for each sample and the Large Counts condition is also met for each sample.

• The Random condition is met for each sample but the Large Counts condition is not met for at least one sample.

• The Random condition is not met for each sample, but the Large Counts condition is met for each sample.

A recent Pew Research Center poll asked random samples of working women and men how much they value job security. Of the 806 women, 709 said job security was very or extremely important, compared to 802 of the 944 men surveyed. Construct a 95% confidence interval for the difference in the proportion of all working women and men who would consider job security very or extremely important.

• (0.85, 0.88)

• (0.03, 0.032)

• (-0.002, 0.062)

• (.223, .262)

A recent Pew Research Center poll asked random samples of working women and men how much they value job security. Of the 806 women, 709 said job security was very or extremely important, compared to 802 of the 944 men surveyed. A 95% confidence interval for the difference in the proportion of all working women and men who would consider job security very or extremely important was found to be (-0.002, 0.062). Is there convincing evidence of a difference in the proportion of working women and men who would consider job security very or extremely important?

• Yes. There are more positive numbers in the interval and therefore there is higher proportion of women that feel this way.

• Yes. There are some negative numbers in the interval and therefore there is a higher proportion off men that feel this way.

• No. Since the interval includes both negative and positive values, 0 is within the interval. This means there is not convincing evidence of a true difference in proportions.

• Cannot be determined just from the interval.

The General Social Survey (GSS) is given periodically to randomly selected U.S. adults. One question on the GSS asks respondents about how happy they are. In 2014, 2189 of 2538 adults said they were pretty or very happy, while 1286 of 1484 responded the same way in 1974. Construct a 99% confidence interval for the difference in proportion of (2014 adults - 1974 adults) how happy they are.

• (0.862, 0.867)

• (-0.033, 0.025)

• (0.22, 0.25)

• (-0.15, -0.13)

The National Research Council of the Philippines reported that 210 of 361 members in biology are women, but only 34 of 86 members in mathematics are women. Establish a 95% confidence interval estimate of the difference in proportions of women in biology and women in mathematics in the Philippines.

• (0.071, 0.301)

• (0.032, 0.34)

• (0.292, 0.498)

• (.389, 0.697)

The National Research Council of the Philippines reported that 210 of 361 members in biology are women, but only 34 of 86 members in mathematics are women. A 99% confidence interval estimate of the difference in proportions of women in biology and women in mathematics in the Philippines was found to be (0.035, 0.338). Is there convincing evidence of a difference in proportion of women in biology and women in math in the Philippines?

• Yes. Since the entire interval is positive, there is convincing evidence that the proportion of women in biology is higher than women in math in the Philippines.

• Yes. Since the entire interval is positive, there is convincing evidence that the proportion of women in math is higher than women in biology in the Philippines.

• No. Since 0.035 is so close to 0, we can't say there is convincing evidence of a true difference.

• Cannot be determined from just an interval.

In a simple random sample of 300 elderly men, 195 were married, while in an independent simple random sample of 400 elderly women, 192 were married. Determine a 99% confidence interval estimate for the difference between the proportions of elderly men and women who are married.

• (0.097, 0.243)

• (0.07, 0.27)

• (0.11, 0.23)

• (0.46, 0.67)

In a simple random sample of 300 elderly men, 195 were married, while in an independent simple random sample of 400 elderly women, 192 were married. A 99% confidence interval estimate for the difference between the proportions of elderly men and women who are married was found to be 0.07 to 0.27. Is there convincing evidence of a true difference in proportion of elderly men and women who are married?

• Yes. Since the entire interval is positive, there is evidence that a higher proportion of men are married.

• Yes. Since the entire interval is positive, there is evidence that a higher proportion of women are married.

• No. Since 0.07 is really close to 0, there is not convincing evidence of a true difference.

• Cannot be determined from just an interval.

Consider a random sample of 100 females and 100 males. Suppose 15 of the females are left-handed and 12 of the males are left-handed. What is the 90% confidence interval. for the difference between population proportions of females and males who are left-handed (females − males)?

• (-0.09, 0.15)

• (-0.06, 0.12)

• (-0.05, 0.11)

• (0.12, 0.15)

A random sample of 100 females and 100 males is taken and 15 of the females are left-handed and 12 of the males are left-handed. A 90% confidence interval for the difference between population proportions of females and males who are left-handed (females − males) is found to be -0.05 to 0.11. Is there convincing evidence of a true difference in proportion of female and males that are left-handed?

• Yes. Since most of the interval is positive, there is a higher proportion of females that are left-handed.

• Yes. Since there are negative values within the interval, there is convincing evidence that a higher proportion of males that are left-handed.

• No. Since the interval contains both negative and positive values, 0 is within the interval. This means there is not convincing evidence of a true difference in proportion.

• Cannot be determined from just an interval.