Remember that there is variability associated with your outcomes and statistics. Show
When you calculate a statistic based on your sample data, how do you know if the statistic truly represents your population? Even if you've selected a random sample, your sample will not completely reflect your population. Each sample you take will give you a different result. Let's Look at an Example:Suppose that you want to compare the mean age for those with and without an IV in the prehospital setting. You review the ambulance runs for the past two weeks and calculate a mean age of 10.4 years for those with an IV and 8.5 years for those without an IV. The difference between the two means is 1.9 years. From this, you might conclude that those receiving an IV were older on average. Suddenly, it's not clear that there's an important difference in age between these two groups. Now suppose you collect the same data over the next six weeks. This time the average age for those with an IV is 9.2 years and the average age for those without an IV is 8.9 years, for a difference of 0.3 years. Suddenly, it's not clear that there's an important difference in age between these two groups. Why did your different samples yield different results? Is one sample more correct than the other? Remember that there is variability in your outcomes and statistics. The more individual variation you see in your outcome, the less confidence you have in your statistics. In addition, the smaller your sample size, the less comfortable you can be asserting that the statistics you calculate are representative of your population. Providing a Range of ValuesA confidence interval provides a range of values that will capture the true population value a certain percentage of the time. You determine the level of confidence, but it is generally set at 90%, 95%, or 99%. Confidence intervals use the variability of your data to assess the precision or accuracy of your estimated statistics. You can use confidence intervals to describe a single group or to compare two groups. We will not cover the statistical equations for a confidence interval here, but we will discuss several examples. Example The confidence interval in the above example could be described at 94 to 108 bpm (beats per minute) or 101 bpm ± 7 bpm. Here the number 7 is your margin of error. For confidence intervals around the mean, the margin of error is just half of your total confidence interval width. Sample Size and VariabilityThe precision of your statistics depends on your sample size and variability. A larger sample size or lower variability will result in a tighter confidence interval with a smaller margin of error. A smaller sample size or a higher variability will result in a wider confidence interval with a larger margin of error. The level of confidence also affects the interval width. If you want a higher level of confidence, that interval will not be as tight. A tight interval at 95% or higher confidence is ideal. Examples:  rev. 04-Aug-2022 Related Statistics Q&AFind answers to questions asked by students like you. Q: What happens to the interval as you increase the confidence of the sampling distribution? A: As the confidence level increases the width of the confidence interval increases and as the… Q: The mean of the distribution of sample means would be equal to: A: The mean of the distribution of sample means would be equal to ? 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Explain whether or not this… A: Given : Assertion : As the sample size increases, standard error of the mean decreases Q: The population standard deviation for the heights of dogs, in inches, in a city is 6.7 inches. If we… A: Click to see the answer Q: If you want to be 95% confident of estimating the population mean to within a sampling error of ±4… A: We have given that Margin of error = E= ±4 Standard deviation = 13 95%confidence. Q: An advertising executive wants to estimate the mean amount of time that consumers spend with digital… A: Answer - The standard deviation σ = 47 minutes. 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The z-critical value for 99% confidence interval is 2.5758… Q: a)What assumption regarding the population is necessary for making an interval estimate for the… A: When we carry out parametric tests we assume that the population follows a distribution that is we… Q: The quartiles of any distribution are the 25th and 75th percentiles. About how many standard… A: 25th Percentile = P(Z <z ) = 0.25 For normal table P(Z < -0.67 ) = 0.2514 Hence, 25th… Q: If you want to be 99% confident of estimating the population mean to within a sampling error of ±20… A: Click to see the answer Q: A university dean of studentswishes to estimate the average number of hours studentsspend doing… A: Click to see the answer Q: If you want to be 95% confident of estimating the population mean to within a sampling error of ±4… A: We are interested in the finding sample size for the given margin of error and confidence level. Q: An irate student complained that the cost of textbooks was too high. He randomly surveyed 36 other… A: Find best point estimate. Q: The area of the rectangle depicting a uniform distribution is always equal to the mean of the… A: The area of rectangle depicting a uniform distribution is not always mean of the distribution. Q: You would like to make an interval estimate of a population mean from a sample of size 25. Assume… A: The random variable X follows normal distribution. It is given that, the sample size is 25. The… Q: If you want to be 99% confident of estimating the population mean to within a sampling error of ±6… A: Given that Population SD = 16 Error, E = 6 Confidence level = 99% The critical value of Z at 99%… Q: the mean and standard deviation of a population are 200 and 20 respectively. suppose the sample size… A: Given data, Mean=200 sd=20 If n=36 the mean of the sampling distribution=? Q: the mean and standard deviation of a population are 200 and 20 respectively. suppose the sample size… A: Given dataμ=200σ=20If n=36 the mean of the sampling distribution=? Q: the mean and standard deviation of a population are 200 and 20 respectively. suppose the sample size… A: Given data,μ=200σ=20If n=36the mean of the sampling distribution=? Q: If you want to be 99% sure confident of estimating the population mean to within a sampling error of… A: The critical value from the standard normal table at 99% confidence level is, Q: Based on this graph what was the approximate distribution of the averages? X~___(___,___) A: Central limit theorem (CLT): According to CLT, for a given sufficiently large sample size from a… Q: If you want to be 95% confident of estimating the population mean to within a sampling error of ±2… A: Click to see the answer Q: find the standard deviation for: 25% of students who took an examination scored more than 73 in an… A: The standard deviation for 25% of students who took an examination scored more than 73 in an… Q: For an educational study, a volunteer must place in the middle 50% on a test. If the mean for the… A: Click to see the answer Q: For any distribution what is the score that separates the highest 10% from the rest called? A: Click to see the answer Q: Heights for women are bell-shaped with a mean of 65 inches and a standard deviation of 2.5 inches.… A: Click to see the answer Q: A market researcher wants to estimate the amount of money that a Christmass hopper will spend on… A: Click to see the answer Q: For a medical study, a researcher wishes to select people in thr middle 75% of the population based… A: Introduction: Definition: Z-score A Z-score is a numerical measurement that describes a value's… Q: In a certain distribution of numbers, the mean is 100 with a standard deviation of 2. At least what… A: Given data, μ=100σ=2P(90<X<110)=? Q: The average number of calories in a regular-size bagel is 240. If the standard deviation is 38… A: The Chebyshev’s rule is given below. Q: when we sample from an infinite population, what happens to the standard error of the mean if the… A: Given: Initial sample size = 1600 New sample size = 100 Q: A researcher is interested in estimating the average salary of teachers in a large urban school… A: Click to see the answer Q: A population was found to have a mean of µ =75 and standard deviation of σ =2.3. If you took every… A: Given information- Population mean µ = 75 Population standard deviation, σ = 2.3 Sample size, n = 10 Q: Let’s assume that weight is normally distributed with a mean of 160 and a standard deviation of 25… A: Step-by-step procedure to obtain the middle 80% 0f all people lie between which two weights using… Q: What formula is used to gain information about a sample mean when the variable is normally… A: Sample size: It is the number of observations in a sample under consideration. By increasing the… What happens to the interval when the sample size is increased?Increasing the sample size decreases the width of confidence intervals, because it decreases the standard error.
Does larger sample mean larger confidence interval?A larger sample size or lower variability will result in a tighter confidence interval with a smaller margin of error. A smaller sample size or a higher variability will result in a wider confidence interval with a larger margin of error. The level of confidence also affects the interval width.
What is large sample interval estimators?Large Sample (Approximate) Intervals
are approximate 95% confidence intervals for the parameters that the point estimates estimate, when the appropriate conditions are satisfied. The sample size is large (both sample sizes are large in the two-sample cases).
What is the effect of a larger sample size on the interval estimate larger sample provides a select your answer margin of error?Answer: As sample size increases, the margin of error decreases. As the variability in the population increases, the margin of error increases. As the confidence level increases, the margin of error increases.
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In interval estimation, as the sample size becomes larger, the interval estimate __________.
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