Measuring Usability: Sample Size Calculator for a Completion Rate

Sample Size Calculator for a Completion Rate
by Jeff Sauro | January 4, 2008 :: 60 Related Questions How useful was this calculator?
Avg. Rating: 48 ( 5 ) | 8 Comments

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Sample Size	45
Calculator	25
Confidence Intervals	20
Completion Rate	18
Graph	10

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Use this calculator to understand how sample size changes will affect the confidence interval around a completion rate. For more context, see the Sample Size article.

Known Users: Most Likely Completion Rates

Known Minimum Completion Rate: Unknown Users

The calculations are derived from the Adjusted-Wald binomial confidence interval.

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	My question is really about sample size. Say you work at a facility and want to perform an assessment of your safety culture – this would involve multiple topics of questions expecting answers like agree, tend to agree, not sure, tend to disagree, disagree. How would you estimate the sample size if your total facility population is only 80 persons? Would the manner in which you estimate the sample size be different if you used any combination of the following methods to conduct the assessment: a written survey, individual interviews, one on one observations, or focus groups? What if these assessments must be performed at eight different facilities that have no relationship to each other and each of their total populations range from 15-1000, with a mean of 153? To make it even more complicated, would the manner in which you estimate sample size change if you really wanted each of the facilities to assess eight work groups or divisions in the workforce (e.g., management, operations, maintenance, engineering, etc.) at each of their facilities? Greatly appreciate your input.
	Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $30,000 and $45,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. What is the planning value for the population standard deviation (0 decimals)?
	A researcher is interested in estimating the average salary of fire fighters in a large city. He wants to be 95% confident that his estimate is correct. If the standard deviation is $1050, how large a sample is needed to get the desired information and to be accurate within $200?
	In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security relatd jobs and found that 1,143 were positive a. construct a 95% confidence interval for the population proportion of positive drug test. b. why is the normality assumption not a problem, despite the very small value?
	A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on very accurate scale. The results in grams were 3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477 (a)Construct a 90% confidence intervalfor the true mean weight. (b)What sample size would be necessary to estimate the true weight an error of +/- 0.03 gram with 90% confidence?
	A researcher expects the population proportion of the Cubs Fans in Chicago to be 80%. Error of less than 5% confident of an estimate to be made from a mail survey. What is the sample size required?
	A random sample of n=64 children of working mothers showed that they were absent from school an average of 5.3 days per term, with a standard deviation of 1.8 days. Provide a 96% confidence interval for the average number of days absent for all students.
	Linemarking for parking bays shall be determined by the retroreflectivity performance of glass beads in the linemarking. The linemarking average level of reflectivity over the City is to be not less than 100 mcd/sqm/lx and the minimum aceptable reflectivity is 80 mcd/m2/lx. Conduct a quarterly assessment of roadmarking condition, randomly sampling 5% of the City Roads each quarter so that 20% of all the roadmarkings are assessed each year. The results shall produce the results specified below. The methods used to perform the assessment shall be sufficient to produce a confidence interval of +/- 5% with a level of confidence of 95%; (a)Average retroreflectivity for the roadmarking (b)Percentage of roadmarking that are below the minimum acceptable standard. The recordings of roadmarkings for the second quarter are as follows: 260.00 263.00 254.00 180.00 174.00 229.00 230.00 56.00 209.00 260.00 309.00 359.00 389.00 491.00 202.00 387.00 440.00 Thanks again
	The Web-based company Oh Baby! Gifts has a goal of processing 95 percent of its orders on the same day they are received. If 485 out of the next 500 orders are processed on the same day, would this prove that they are exceeding their goal, using á = .025? (See story.news.yahoo.com accessed June 25, 2004.)
	When calculating confidence interval estimates...how is the x and standard deviation calculated?
	Philadelphia is conducting a study on the characteristics of tourists who drive to Eagles football games. Previous studies indicate that approximately 70% of all game attendees are people who decided to drive from out of town. If the researcher leading the study desires a 99% confidence level and an interval range of plus or minus 10%, what size should the sample be?
	Calculate the 95% confidence interval on the following GPA's from 30 randomly selected students. 0.979 0.891 0.962 0.858 0.909 0.936 0.963 0.903 0.914 0.925 0.867 0.888 0.735 0.897 0.851 0.776 0.999 0.967 0.503 0.711 0.963 0.943 0.396 0.951 0.747 0.933 0.909 0.583 0.95 0.756
	Popcorn kernels take between 100 and 200 seconds to pop. What sample size (number of kernels) would be needed to estimate the true mean seconds to pop with and error of 5 seconds and 95% confidence level?
	Jeff: Can you possibly share the actual formula you are using in this application to produce the Adjusted Wald calculations? Thanks
	How to determine the sample size for comparing mulltiple parameters like Height , weight, Blood pressure , Blood parameters like blood glucose, total cholesterol, etc in two different populations?
	A telescope manufacturer wants its telescopes to have standard deviations in resolution to be significantly below 2 when focusing on objects 500 light-years away. When a telescope is used to focus on an object 500 light years away 30 times, the sample standard deviation turns out to be 1.46. a.State explicit null and alternate hypotheses b.Test your hypothesis at the á=0.01 level.
	The width of a confidence estimate for a proportion will be: a. Narrower for a 99% confidence interval than for a 95% confidence interval. b. Wider for a sample size of 100 than for a sample size of 50. c. Narrower for 90% confidence than for 95% confidence d. Narrower when the sample proportion is .50 than when the sample proportion is .20.
	Determine the critical value Za/2 that corresponds to 94% level of confidence Compute the 90% confidence interval about m if the sample size, n, is 55. How does does increasing the sample size affect the margin of error, E?
	Suppose you are planning a sample of employees to determine the monthly average # of vacation days. Standards set: Confidence level of 99% and an error of less than 5 units. Standard deviation be 6 units. What would be the required sample size?
	In a survey of 500, 60% responded positively to an value question. Calculate a confidence level at 95% to get an interval estimate for proportion?
	Why don't statisticians calculate 100% confidence intervals?
	How can I compute a one-sided 97.5% confidence interval using SPSS for this ? IN a cohort of 121 eyes treated with drug A, 3 eyes experience a drug related side effect, i.e 3/121. Thanks
	Find the margin or error for the 95% confidence interval used to estimate the population proportion. In a survey of 7100 TV viewers, 38% said they watch network news programs.
	In a national wide survey a researcher expects 30 percent of the population will agree with an value statement. He wishes to have less than 2% error and 95% confident. What sample size is needed??
	When estimating the mean of a population, how large must the sample be in order that the 95% error margin is 1/8 the standard deviation?
	Survey to determine what proportion of new car buyers continue to have their car serviced at the dealership after warranty ends. Estimates 30% of customer do so. Results should be accurate within 5%. Also 95% confident of the results. What sample size is necessary?
	Briefly describe the concept of a confidence interval and provide an example.
	Hi Jeff thanks for all your help so far, your answers have been great and very timely. It is great to be able have help from someone with great professionalism as yourself. I have another question which I am unsure as how to tackle it. I hope you can help me once again – thanks. So here goes. For traffic signs, measurement of retro reflective performance with a reflectometer will be needed as well as visual assessment during Street Surveillance inspections. The Service provider (that’s me!) shall collate and report on the results of actual reflectivity readings for all signs visually identified as required a measured reflectivity assessment to ensure that the Contract Manager and the Service provider have confidence in the visual assessment of retro-reflective performance. The Service provider shall ensure that its procedures to determine the retro reflective performance of Signs provide valid assessments. (So what we have done is taken random readings of various signs for the quarter, see below.) The Australian Standards for these signs states that for Class 1W signs the minimum level of luminous intensity for white, yellow & red signs are 380, 265 & 75 respectively which are to replace the old standard Class 1 signs; white, yellow and red of min. levels of 250, 75 & 50 respectively.(This is a works in progress. It was not noted when taking the readings whether the signs were the new or old standard? I assume the the old standard signs would be the ones with readings of lower values? But they could also be old faded signs with low readings. Do we need to separate the two classes of signs or should we just keep it simple with a general observation?) Further more there are also Class 2 signs which the standards state that the minimum luminous intensity for white, yellow & red signs are 70 50 & 14 respectively. Finally there is one other question which I don’t believe we are in the position to answer without further historical data but I would appreciate your comments. The question asks to assess and report on the degradation of reflectivity performance as a method of predicting the future reflectivity performance of signs. Both Class1 sign readings are: Reflectivity Colour 91.9 W 277 W 403 W 514 W 458 W 97.7 W 520 W 416 W 481 W 508 W 448 W 516 W 282 W 264 W 240 W 276 W 262 W 258 W 296 W 211 W 183 W 46.5 R 45.1 R 80 R 381 R 235 R 35.9 R and for Class2: Reflectivity Colour 32.1 Y 51.4 Y 5.7 Y 41.2 W 45.3 W 79.2 W 52.1 W 54.8 W 63.5 W 22.1 W 60.4 W 77.9 W 78 W 81.6 W 78 W 68.2 W 66.4 W 21 W 72.5 W 3.1 W 50.1 W 106 W 87.4 W 85.3 W 18.1 W 78.9 W 62.5 W 64.5 W 61.2 W 76.9 W 82 W 24.5 W 65.5 W 19.6 W 48.5 W 22.4 W 48.4 W 79.9 W 40 W 84.2 W 7.4 W 45.4 W 80 W 9 W 86.2 W 70.2 W 80.3 W 87.4 W 105 W 86.3 W 11.4 R 26.5 R
	A central university has a student population of 60,000. The university is interested in determining what proportion of them is in favour of a new grading system. Determine a sample size with confidence level of 95% that will show the true proportion of population in favour of the new system within plus and minus 0.02.
	Calculate a 98% confidence interval for the following data 15.7,15.7,15.5,15.2,15.2,15.1,15.3.
	A random sample of 25 households finds that an average of 2.3 people reside in each house (the standard deviation is 0.35). With a 95% confidence level, what is your estimation of the population average?
	A machine produces 3 inch nails. A sample of 100 nails is selected, and it is found that 25 are shorter than 3 inches. Find the 95% confidence interval on the proportion of all such nails that are shorter than 3 inches.
	What is the Z score of a 98% confidence interval?
	In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive. (a) Construct a 95 percent confidence interval for the population proportion of positive drug tests. (b) Why is the normality assumption not a problem, despite the very small value of p?
	A central university has a student population of 60,000. The university is interested in determining what proportion of them is in favour of a new grading system. Determine a sample size with confidence level of 95% that will show the true proportion of population in favour of the new system within plus and minus 0.02.
	in a sample of 1000 tv vieweres 330 watched a particlar programme. find 99 pecent confidence limits for tv viewers who watched this programme
	As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86. a)Construct a 90% confidence interval for the proportion of all kernels that would not pop. b)Check the normality assumption. c) Try the Very Quick Rule. Does it work well here? Why, or why not? d) Why might this sample not be typical?
	I am trying to do A/B testing onweb page displays. One is the test the other is the control. Could you help me determine the formula for sample size at a 95% confidence level? My historical Conversion Rate (success): 11% Visitors: 280 per day I would like to see a 2% improvement in my conversion rate.
	what is the value of z score required for a 70% confidence interval?
	I am charged with sampling expense report submissions for accuracy. We get 8000 T&E claims, and want to sample a subset making inferences about the population. I can probably get a good estimate of the populations' SD, how would i calculate required sample size? I think i would be measuring the delta between actual and claimed - the majority be 0. Is this a one sided issue? Thanks in advance - FT Also, would i need the acceptable level first? ie. we would accept an average difference of $5? How can i work backwards if the first sample size yields an average of $1? (if that made sense)
	How do you determine the sample size for data for which the mean and standard deviation are not known?
	Use the given degree of confidence and sample data to construct a confidence interval for the population mean x. Assume that the population has a normal distribution. The principal randomly selected six students to take an aptitude test. Their scores were: 77.9 89.1 80.7 78.6 74.4 82.0 Determine a 90 percent confidence interval for the mean score for all students. 76.36 < x < 84.54 84.64 < x < 76.26 76.26 < x < 84.64 84.54 < x < 76.36
	An engineer in an automotive factory wishes to know what the tire pressure is on all cars leaving the factory. She measures the tire pressure on a sample of 10 randomly selected cars as they are about to leave the plant, in psi. The results are: 32.1 32.3 32.0 30.9 31.5 32.4 32.9 33.1 32.2 31.4 Calculate a 95% Confidence Interval on these numbers
	Assume that the heights of 5 year old boys are normally distribued with a mean of 100cm and a standard deviation of 60. What is the sampling distribution of the mean for a sample size of 900 and its confidence interval at the 99% level?
	An engineer in an automotive factory wishes to know what the tire pressure is on all cars leaving the factory. She measures the tire pressure on a sample of 10 randomly selected cars as they are about to leave the plant, in psi. The results are: 32.1 32.3 32.0 30.9 31.5 32.4 32.9 33.1 32.2 31.4 Calculate a 95% Confidence Interval on these numbers
	how to calculate one sided 95% confidence limits for a proportion.could you provide a formula
	Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $30,000 and $45,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. What is the planning value for the population standard deviation (0 decimals)? __________ How large a sample should be taken if the desired margin of error is as shown below (0 decimals)? a. $500? __________ b. $200? __________ c. $100? __________ d. Would you recommend trying to obtain the $100 margin of error? _________________
	Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86. (a) Construct a 90 percent confidence interval for the proportion of all kernels that would not pop. (b) Check the normality assumption. (c) Try the Very Quick Rule. Does it work well here? Why, or why not? (d) Why might this sample not be typical?
	If 350 respondents out of a random sample of 1,000 Americans reported that they did not trust their government, what is your estimation at a 99% confidence level of the proportion of the American population who do not trust their government?
	Find a confidence interval for the mean assuming that each sample is from a normal population. Mean = 127, s = 27, n = 16. Find the 90% Confidence Interval.
	A sample of the math test scores of 35 fourth-graders has a mean of 82 with a standard deviation of 15. Find the 95% confidence interval of the mean math test scores of all fourth-graders. Find the 99% confidence interval of the mean math test scores of all fourth-graders. Which interval is larger? Explain why.
	How would I figure out a 90% and 95% confidence interval for the below informaion? What would be the formula? Can I figure this out in Excel or Megastat? How would I do that? Men Female count 53 47 mean 36,492.92 24,451.51 sample variance 340,313,003.72 154,893,232.30 sample standard deviation 18,447.57 12,445.61 standard error of the mean 2,533.97 1,815.38
	An automobile manufacturer wants to estimate the mean gasoline mileage that its customers will obtain with its new compact model. How many sample runs must be performed in order that the estimate be accurate to within 0.25 mpg at 90% confidence? (Assume that ó = 2.0.)
	out of a random sample 167 students pass an exam out of the 300. how do you calculate an exact 99% confidence interval for the proportion of sudents who passed the exam?
	State the main points of the Central Limit Theorem for a mean. B. Why is population shape of concern when estimating a mean? What does sample size have to do with it?
	Administrative staff based at a business school in the UK are advised to take a 15 minute break from their personal computer after working on it for 90 minutes continuously. A random sample of 36 staff revealed that, one average a break was taken after 97.4 minutes of continuous use. The corresponding standard deviation was measured at 5.1 minutes. a. Provide a 99% confidence interval for the population mean time for working on a PC continuously, prior to taking a break. b. Conduct a suitable test at the 1% level of significance, to see whether staff, on average, are working longer than advised.
	A sample of 20 pages was taken without replacement from the 1,591-page phone directory Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was measured (a display ad is a large block of multicolored illustrations, maps, and text). The data (in square millimeters) are shown below: 0 260 356 403 536 0 268 369 428 536 268 396 469 536 162 338 403 536 536 130 (a) Construct a 95 percent confidence interval for the true mean. (b) Why might normality be an issue here? (c) What sample size would be needed to obtain an error of ±10 square millimeters with 99 percent confidence? (d) If this is not a reasonable requirement, suggest one that is. I am new at this and it would help if you could give me the formula and break it down step by step so I can understand. Thanks
	Your company asks you to compare a new advertising campaign and the old one. Sample data on the accounts as follows: Old: 40, 28, 35, 38, 31, 42, 26, 44, 29, 43 New: 29, 26, 31, 26, 28, 31, 19, 21, 27, 30 Calculate the mean, median, and mode. Calculate variance and standard deviation for each set. Calculate a 95% Confidence Interval for the two sets.
	Based on information obtained from a sample of 54, a 98% confidence interval for the average profit level of regional banks is given by 67.4 million to 87.78 million. Determine the sample standard deviation of profit
	Can you give me a formula to calculate sample size?

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June 24, 2009 | Ofori Boateng wrote:

I am about looking to determine my sample size of how many managers I should select to from six companies for my survey so that my sample size and frame will be valid. Unfortunately I do not have the total number of managers that are working for these phone companies in Ghana and it is becoming increasing difficult for me to find the numbers. Is there a way for me to determine this unknown sample size. The tpye of managers I need for my survey are those in operations research, financial operations, and makerting department. Please try and help me here. Thank you. Ofori Boateng

June 6, 2009 | Thomas Smith wrote:

) "Why is population shape of concern when estimating a mean? What does sample size have to do?"

June 6, 2009 | Thomas Smith wrote:

The mean of a data sample, size n, forms an approximately normal distribution. ... Sample size n is about 30 to be sure that the central limit theorem applies.

June 6, 2009 | Thomas Smith wrote:

In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive. (a) Construct a 95 percent confidence interval for the population proportion of positive drug tests. (b) Why is the normality assumption not a problem, despite the very small value of p?

June 6, 2009 | Thomas Smith wrote:

A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were 3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477 (a) Construct a 90 percent confidence interval for the true mean weight. (b) What sample size would be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence? (c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture.

April 16, 2009 | Brad Woodruff wrote:

What is the best way to calculate sample size for an incidence rate, such as a mortality rate?

February 10, 2009 | theresa wood wrote:

3. A researcher is interested in estimating the average salary of fire fighters in a large city. He wants to be 95% confident that his estimate is correct. If the standard deviation is $1050, how large a sample is needed to get the desired information and to be accurate within $200?

May 17, 2008 | Chris wrote:

How do you calculate a confidence interval when the population standard deviation is unknown?

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