This is the idea for what we'll be doing. But the other 19 (or 95% of them) do contain the real value. You can see that 1 of the 20 (5%) confidence intervals doesn't contain the actual value of 68.5% (based on data from ). Here's a visual for 20 theoretical samples and corresponding confidence intervals for the proportion who work: The idea behind a certain % (like 95%) is that we're saying we'll be right 95% of the time. See, every time we get a new sample, we have a new estimate, and hence a new confidence interval. If we say that we're 95% confident that the real proportion is somewhere between 61% and 69%, we're saying that if we were to repeat this with new samples, and gave a margin of ±4% every time, our interval would contain the actual proportion 95% of the time. We might take a sample of 100 individuals and find a sample proportion of 65%. The idea of a confidence interval is this: Suppose we're wondering what proportion of ECC students are part-time. The notation we use is for the confidence interval. The level of confidence is the expected proportion of intervals that will contain the parameter if a large number of samples is maintained. Similarly, the average number of hours worked per day of 7.6 is a point estimate the average number of hours worked per day for all employed persons.Ī confidence interval estimate is an interval of numbers, along with a measure of the likelihood that the interval contains the unknown parameter.
50%, for example, is the point estimate for the percentage of all Latinos who feel that way. The news release isn't saying that the average of time spent for all employed persons is 7.6 hours per day - they're referring to those in the sample of 12,250 individuals in the study.īoth of these examples are called point estimates. They worked longer on weekdays than on weekend days - 7.9 versus 5.6 hours. In a similar manner, consider one of the results from the American Time Use Survey: Employed persons worked an average of 7.6 hours on the days that they worked. For example, when the report says that half of all Latinos say that the situation is worse now than it was a year ago, it's not saying that they actually asked every single Latino living in the United States. The whole point of collecting information from a sample is to gain some information about the population. How did they determine that the margin was ☒.8%? The Logic of Confidence Intervals
#Finding p hat of two stats stat crunch full
(Source: Pew Research)įurther down that particular article, there's another interesting line: The margin of error for the full sample is plus or minus 2.8 percentage points for registered voters, the margin of error is 4.4 percentage points. Half (50%) of all Latinos say that the situation of Latinos in this country is worse now than it was a year ago, according to a new nationwide survey of 2,015 Hispanic adults conducted by the Pew Hispanic Center. In Section 8.2, saw the following excerpt from a report by the Pew Research Foundation: Hispanics See Their Situation in U.S. It has a margin of sampling error of plus or minus 4 percentage points. The telephone poll of 602 likely Michigan voters was conducted Sept. The EPIC-MRA poll conducted for The Detroit News and television stations WXYZ, WILX, WOOD and WJRT found 50 percent of likely Michigan voters support the stem cell proposal, 32 percent against and 18 percent undecided. pollĪ recent poll shows voter support leading opposition for ballot proposals to loosen Michigan's restrictions on embryonic stem cell research and allow medical use of marijuana. Stem cell, marijuana proposals lead in Mich. Margins of error range from +/-3 to 4 percent. On average, 46 percent say that al Qaeda was behind the attacks while 15 percent say the US government, seven percent Israel, and seven percent some other perpetrator. International Poll: No Consensus On Who Was Behind 9/11Ī new poll of 17 nations finds that majorities in only nine of them believe that al Qaeda was behind the 9/11 terrorist attacks on the United States. The margin of error of the survey is plus or minus 2.8 percentage points at the 95% confidence level. Perhaps the most common confidence intervals that we see in the news are regarding proportions.
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