Prayer in school A New York Times/CBS News Poll asked the question, “Do you favor an amendment to the Constitution that would permit organized prayer in public schools?” Sixty-six percent of the sample answered “Yes.” The article describing the poll says that it “is based on telephone interviews conducted from Sept. 13 to Sept. 18 with adults around the United States, excluding Alaska and Hawaii. . . . The telephone numbers were formed by random digits, thus permitting access to both listed and unlisted residential numbers.” The article gives the margin of error for a confidence level as percentage points.
(a) Explain what the margin of error means to someone who knows little statistics.
(b) State and interpret the 95% confidence interval.
(c) Interpret the confidence level.
a). On average the sample proportion will be within of the true proportion in 95% of all samples.
b). We are localid="1649754733996" confident that the true population proportion is between localid="1649754744695" and localid="1649754756510" .
c). On average, in localid="1649754767371" of all samples the corresponding confidence interval will contain the true population proportion localid="1649754793252" .
The article gives the margin of error for a confidence level as percentage points.
The margin of error is the amount of error that is made, on average, in estimating the population proportion by the sample proportion .
Thus on average the sample proportion will be within of the true proportion in of all samples.
The article gives the margin of error for a .
The boundaries of the confidence interval is the sample proportion increased/decreased by the margin of error:
We are confident that the true population proportion is between and .
The article gives the margin of error for a confidence level.
The confidence level is .
This means: On average, in of all samples the corresponding confidence interval will contain the true population proportion .
Good wood? A lab supply company sells pieces of Douglas fir inches long and inches square for force experiments in science classes. From experience, the strength of these pieces of wood follows a Normal distribution with standard deviation pounds. You want to estimate the mean load needed to pull apart these pieces of wood to within pounds with confidence. How large a sample is needed? Show your work.
- Understand how the margin of error of a confidence interval changes with the sample size and the level of confidence .
Whelks and mussels The small round holes you often see in sea shells were drilled by other sea creatures, who ate the former dwellers of the shells. Whelks often drill into mussels, but this behavior appears to be more or less common in different locations. Researchers collected whelk eggs from the coast of Oregon, raised the whelks in the laboratory, then put each whelk in a container with some delicious mussels. Only whelks drilled into a mussel. The researchers want to estimate the proportion of Oregon whelks that will spontaneously drill into mussels.
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