To construct the 95% confidence interval for the population mean.

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A botanist has produced a new variety of hybrid soybean that is better able to withstand drought. She randomly selected seeds and found that have germinated. You can use Minitab to compute the confidence interval. Select summarized data and enter the number of events and the number of trials Click Options and select the correct confidence level. The first question to ask yourself is: Which parameter are you trying to estimate? If yes, then follow the next 3 steps:.

If you want to construct a confidence interval about the population proportion, follow these 3 steps:. Point Estimates We start with a point estimate.


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We use point estimates to construct confidence intervals for unknown parameters. A confidence interval is an interval of values instead of a single point estimate. The level of confidence corresponds to the expected proportion of intervals that will contain the parameter if many confidence intervals are constructed of the same sample size from the same population. Our uncertainty is about whether our particular confidence interval is one of those that truly contains the true value of the parameter.

The point estimate The point estimate comes from the sample data. The margin of error Depends on the level of confidence, the sample size and the population standard deviation.

Inference: Confidence Intervals – ENV Statistics Review Website

Go to your standard normal table and find the area of 0. What is the Z-score for that area? Figure 4. Normal probability plot. Solution The data is normally distributed. Software Solutions Minitab For Minitab, enter the data in the spreadsheet and select Basic statistics and 1-sample t-test. Excel For Excel, enter the data in the spreadsheet and select descriptive statistics.

Mean 6. The Sample Proportion The sample proportion is the best point estimate for the true population proportion. The Assumption of Normality when Estimating Proportions The assumption of a normally distributed population is still important, even though the parameter has changed. Constructing a Confidence Interval about the Population Proportion Constructing a confidence interval about the proportion follows the same three steps we have used in previous examples. Software Solutions Minitab You can use Minitab to compute the confidence interval. Excel Excel does not compute confidence intervals for estimating the population proportion.

Like the explanation on how to find a confidence interval?

The Starting Point: The Need for a Measurement

Check out our statistics how-to book , with a how-to for every elementary statistics problem type. Watch the video or read the steps below:. The formula for constructing a CI with the t-distribution. Step 2: Subtract 1 from your sample size to find the degrees of freedom df. Set this number aside for a moment. Step 3: Subtract the confidence level from 1, then divide by two. This is your alpha level. Degrees of freedom in the left column of the t distribution table.

Step 5: Divide your std dev step 1 by the square root of your sample size. Step 6: : Multiply step 4 by step 5. Step 7: For the lower end of the range , subtract step 6 from the mean Step 1. Watch the video or read the article below:. There were 6 samples in this experiment.

Step 1: Subtract the confidence level Given as 95 percent in the question from 1 and then divide the result by two. This is your alpha level , which represents the area in one tail. Step 2: Subtract your result from Step 1 from 1 and then look that area up in the middle of the z-table to get the z-score :. Step 4: For the lower end of the range, subtract step 3 from the mean.

Or three. Or there might be a paperwork backlog and it could be a week. So your CI would probably be between 2 and 4 days. This section breaks everything down into simple steps and shows you how to find a confidence interval for population proportions. Of those applicants, 57 were men.

Step 1: Read the question carefully and figure out the following variables :. Step 2: Multiply by. Step 3: Divide step 2 by the sample size. Step 4: Take the square root of step 3 : sqrt 0. Step 6: : For the lower percentage, subtract step 5 from. Step 7: For the upper percentage, add step 5 to. This next method involves plugging in numbers into the actual formula. Confidence intervals for a proportion are calculated using the following formula: The formula might look daunting, but all you really need are two pieces of information: the z-score and the P-hat.

You should be familiar with looking up z-scores from previous sections on the normal distribution if you need a refresher, be sure to watch the above video and P-hat is just dividing the number of events by the number of trials. Step 1: Divide your confidence level by 2 :. Step 2: Look up the value you calculated in Step 1 in the z-table and find the corresponding z-value.

Single-Sample Confidence Interval Calculator Using the Z Statistic

The z-value that has an area of. Your answer can be expressed as: 0. Finding confidence intervals for two populations can look daunting, especially when you take a look at the ugly equation below. It looks a lot worse than it is, because the right side of the equation is actually a repeat of the left! Finding confidence intervals for two populations can be broken down to an easy three steps. Step 3: Enter your data into the following formula and solve:.

CI for the mean formula.


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Sample problem: Calculate the 95 percent confidence interval for the mean in Excel using the following sample: 2,5,78,45,69,,34,,34,36,85,37,37,84,94,,,,,,,45,68,35,56,67,87,,,56, Step 1: Type your data into a single column in Excel. For this example, type the data into cells A1:A Step 3: Enter your input range into the Input Range box. Step 4: Type an output range into the Output Range box. This is where you want your answer to appear. For this sample, the mean Xbar is So the mean has a lower limit of Over the long-term, if you ran tests on many, many samples, there is a 99 percent probability that the calculated intervals would contain the true mean.

Statistics about two populations is incredibly important for a variety of research areas. The confidence interval CI for the difference between the two population means is used to assist researchers in questions such as these. The TI 83 allows you to find a CI for the difference between two means in a matter of a few keystrokes. Step 2: Press 9 to select 2-SampZInt…. Enter the values from the problem into the appropriate rows, using the down arrow to switch between rows as you complete them.

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The answer displayed is 6. Sample problem : A recent poll shows that of Americans have had at least one caffeinated beverage in the last week. Step 5: Arrow down and then enter your n value: This is your confidence level and must be entered as a decimal. The calculator will return the range. Step 4 : Enter Step 5 : Enter Step 7 : Enter. The calculator will give you the result of This is the same as:.