Two friends decided that they could not trust cable news shows to report accurate information about the public’s opinion about legalized abortion. One friend, a regular viewer of a liberal-leaning channel, felt that the public’s support for legalized abortion was overstated in shows on that channel. The other friend, who watched a channel known to cater to conservative viewers, suspected that its shows overstated the public’s opposition to legalized abortion.

The friends teamed up to draw a random sample from their city and ask respondents to rate their support for legalized abortion on a scale from 0 to 10.

Figure 7.26 shows the distribution of responses.

a. How many respondents were in the sample, according to Figure 7.26?

b. Use Figure 7.26 to find the sample mean.

c. If overall mean support for legalized abortion in the friends’ city is 4.95 and the standard deviation is .05, find the probability that the friends would draw another random sample of the same size that falls above the original sample mean that you calculated for Part b.

d. What proportion of the sample collected by the friends strongly supports legalized abortion (9 or 10) or strongly opposes it (0 or 1)?

e. If the actual percentage of people in the friends’ city who hold strong opinions about legalized abortion is 51.5%, find the probability that the friends would draw another random sample of the same size that falls above the original sample proportion that you calculated for Part d.

f. Which is more likely: drawing a random sample larger than the original sample mean or drawing a random sample larger than the original sample proportion?
Give one reason why one is more likely than the other.
g. Do the data support the friends’ suspicion that the news stations they watch overstate support for or opposition to legalized abortion?