Confidence Intervals on Faith Healing
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This question is asking for speculation about the possible results of a study if we change the size of the population. It all depends on unknowns such as how representative the 100 adults are of the population. In general, the larger the population the sure we are that it is representative of the population.
In a poll of 100 adults, 45% reported they believed in "faith healing." (USA Today, 20 April 1998). Based on this survey, a "95% confidence interval" for the proportion in the population who believe in faith healing is about 42% to 48%. If this poll had been based instead on 5000 adults, do you think the "95% confidence interval" would be wider or narrower than the interval given? Please explain how I would interpret/explain in words how the confidence interval is wider than the interval given?
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Solution Summary
The solution examines confidence intervals on faith healing beliefs. The interpretation of the results of the intervals is examined.
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Hello,
As a rule of thumb, the larger your sample, the more confident you are that it represents the general population. The goal of using samples is to approximate the actual population. Now, if we have a small niche market (all university professors in a given school), it would be very important to get a large enough sample size such that your sample is representative of your population. If you have 100 professors and only poll 10 of them, your sample will NOT be representative. Therefore, you will have a very wide confidence interval since you are not sure where your sample actually lies with respect to the population.
Now, what if you ...
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