2 Ways To Reduce Margin Of Error
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as the mean. However, you can use several strategies to reduce the width of a confidence interval and make your estimate more precise. The size of the sample, the variation of the data, the how to reduce margin of error by half type of interval, and the confidence level all affect the width of the how to reduce margin of error statistics confidence interval.In This TopicIncrease the sample sizeReduce variabilityUse a one-sided confidence intervalLower the confidence levelIncrease the sample size Often, the most how to reduce margin of error in confidence interval practical way to decrease the margin of error is to increase the sample size. Usually, the more observations that you have, the narrower the interval around the sample statistic is. Thus, you can often
Reduce Margin Of Error Sample Size
collect more data to obtain a more precise estimate of a population parameter. You should weigh the benefits of increased precision with the additional time and resources required to collect a larger sample. For example, a confidence interval that is narrow enough to contain only the population parameter requires that you measure every subject in the population. Obviously, such a strategy would usually be highly impractical. Reduce variability The how is margin of error calculated in polls less that your data varies, the more precisely you can estimate a population parameter. That's because reducing the variability of your data decreases the standard deviation and, thus, the margin of error for the estimate. Although it can be difficult to reduce variability in your data, you can sometimes do so by adjusting the designed experiment, such as using a paired design to compare two groups. You may also be able to reduce variability by improving the process that the sample is collected from, or by improving your measurement system so that it measures items more precisely. Use a one-sided confidence interval A one-sided confidence interval has a smaller margin of error than a two-sided confidence interval. However, a one-sided interval indicates only whether a parameter is either less than or greater than a cut-off value and does not provide any information about the parameter in the opposite direction. Thus, use a one-sided confidence interval to increase the precision of an estimate if you are only worried about the estimate being either greater or less than a cut-off value, but not both. For example, a beverage company wants to determine that the amount of dissolved solids in their drinking water. The fewer dissolved solids
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of Error How Sample Size Affects the Margin of Error Related Book Statistics For Dummies, 2nd Edition By Deborah J. Rumsey In statistics, the two most important ideas regarding sample size and margin of error http://support.minitab.com/en-us/minitab/17/topic-library/basic-statistics-and-graphs/introductory-concepts/confidence-interval/make-ci-more-precise/ are, first, sample size and margin of error have an inverse relationship; and second, after a point, increasing the sample size beyond what you already have gives you a diminished return because the increased accuracy will be negligible. The relationship between margin of error and sample size is simple: As the sample size increases, the margin of error decreases. This relationship is called an inverse because the two move in http://www.dummies.com/education/math/statistics/how-sample-size-affects-the-margin-of-error/ opposite directions. If you think about it, it makes sense that the more information you have, the more accurate your results are going to be (in other words, the smaller your margin of error will get). (That assumes, of course, that the data were collected and handled properly.) Suppose that the Gallup Organization's latest poll sampled 1,000 people from the United States, and the results show that 520 people (52%) think the president is doing a good job, compared to 48% who don't think so. First, assume you want a 95% level of confidence, so you find z* using the following table. z*-Values for Selected (Percentage) Confidence Levels Percentage Confidence z*-Value 80 1.28 90 1.645 95 1.96 98 2.33 99 2.58 From the table, you find that z* = 1.96. The number of Americans in the sample who said they approve of the president was found to be 520. This means that the sample proportion, is 520 / 1,000 = 0.52. (The sample size, n, was 1,000.) The margin of error for this polling question is calculated in the following way: According to this data, you conclude with 95% confidence that 52% of all Americans approve of the president, plus or minus 3.1%. Using the same formu
a confidence interval estimate of a population mean: sample size, variability in the population, and confidence level. For each of these quantities separately, explain briefly what happens to the margin of error as that quantity increases. Answer: As sample size increases, http://inspire.stat.ucla.edu/unit_10/solutions.php the margin of error decreases. As the variability in the population increases, the margin of error https://www.math.lsu.edu/~madden/M1101/student_work/margin_of_error.html increases. As the confidence level increases, the margin of error increases. Incidentally, population variability is not something we can usually control, but more meticulous collection of data can reduce the variability in our measurements. The third of these--the relationship between confidence level and margin of error seems contradictory to many students because they are confusing accuracy (confidence level) and precision (margin margin of of error). If you want to be surer of hitting a target with a spotlight, then you make your spotlight bigger. 2. A survey of 1000 Californians finds reports that 48% are excited by the annual visit of INSPIRE participants to their fair state. Construct a 95% confidence interval on the true proportion of Californians who are excited to be visited by these Statistics teachers. Answer: We first check that the sample size is large enough to apply margin of error the normal approximation. The true value of p is unknown, so we can't check that np > 10 and n(1-p) > 10, but we can check this for p-hat, our estimate of p. 1000*.48 = 480 > 10 and 1000*.52 > 10. This means the normal approximation will be good, and we can apply them to calculate a confidence interval for p. .48 +/- 1.96*sqrt(.48*.52/1000) .48 +/- .03096552 (that mysterious 3% margin of error!) (.45, .51) is a 95% CI for the true proportion of all Californians who are excited about the Stats teachers' visit. 3. Since your interval contains values above 50% and therefore does finds that it is plausible that more than half of the state feels this way, there remains a big question mark in your mind. Suppose you decide that you want to refine your estimate of the population proportion and cut the width of your interval in half. Will doubling your sample size do this? How large a sample will be needed to cut your interval width in half? How large a sample will be needed to shrink your interval to the point where 50% will not be included in a 95% confidence interval centered at the .48 point estimate? Answer: The current interval width is about 6%. So the current margin of error is 3%. We want margin of error = 1.5% or 1.96*sqrt(.4
a response to the following: You are a political consultant who has been asked to predict the winner in what is expected to be a very close race for a senate seat. There are two candidates: a democrat and a republican. A previous poll of a random sample of people who are likely to vote has found 49% of the sample favor the democrat. The poll has a reported margin of error of plus or minus 4%, at 95% confidence. Explain how you might use a computer simulation to determine how large a sample you would need to reduce the margin of error to 2%. If the poll were repeated with a sample of this size, would you necessarily get a better basis for predicting a winner? Here is what they said. Student responses are in black. My remarks are in red. To see how I would have answered, look at the end of this document. -In order to reduce the margin of error, increase the number of people polled along with the number of samples. More individuals in a sample, or more samples, both will yield more information. But when we speak of "margin of error," we generally mean to refer to a single sample. -Yes. With each time (averaged w/ the others), the margin of error as well as the confidence would increase. You should note that there is a tradeoff between margin of error and level of confidence. Even with a single sample, your margin of error can be made smaller at the expense of confidence. -In order to gain a 2% margin of error, you must sample a large enough group of the population. You must sample until less than 5% of the sample group is further away than 2% from the target value. This statement doesn't make any sense in the context. The sampled units are being tested to see if they are democrats or republicans. How could an individual be "2% from the target value"? The previous sentence is a misunderstanding of what is meant by level of confidence. The correct idea