Example questions pertaining to use of Sampling Webulator for a Population Proportion

These questions relate to the computation of sample size from a population proportion based on notes from the Sampling Module.

Use the on-line webulator "sample size for a population proportion" located at (http://health.ahs.upei.ca/webulators/SSprop.php) to compute the required sample size in the following questions
If the value generated is NaN please just click again!

QUESTION #1
Recently the Mayor of the Town of Larsenville (population N) was interested in measuring the use of outdoor swimming pools during the months of July and August. The mayor felt that the pools were under-used and should be closed. However, before removing support for the facilities from the next budget (due in March, 2013), the Mayor suggested that a survey should be conducted to determine the true number of residents of Larsenville using the pools.
Reports from other cities indicated that about ??? percent of residents used the municipal pools during the months of July and August.

Your task is to tell the Mayor how many questionnaires he should use to collect a sample that is representative of the true population.

Remember, the Mayor wishes to be ninety-five percent confident that his sample is within ??? percent of the true population.
The data you need for this task are: the starting population (N = ? ), the proportion of the population that is typically using municipal pools in other cities which you can acquire from other studies, the z score for 95 percent confidence (Zalpha=1.96), and the amount of accuracy for the estimate: recall the Mayor wanted to be within ??? percent of the true population estimate

Click the following random number generator (POP1) to compute the Population of the town of Larsenville

The proportion of the population that is typically using municipal pools in other cities

The Mayor wishes to use an alpha level of 0.05 (notice an explicit beta level is not requred in the application of this webulator),

and he expects that the difference between the estimate of the sample proportion and the TRUE population estimate is within percent. Your task is therefore to determine the number of individuals that should be interviewed.

The data you need for this task are:

• The starting population estimate
• the estimated proportion expected which is a value drawn from previous studies
• the z score for the alpha term (notice beta is not used in this formula)
• the percent difference between your estimates and estimates of the true population proportion.

Click here to access the Webulator for sample size for a population proportion

QUESTION #2
In 1979, the Three Mile Island (TMI) nuclear power plant suffered a major accident and was immediately closed, to prevent melt down and further environmental damage. Several individuals that had residences within a 100 km proximity to the facility reported increased symptom reporting, a higher use of over the counter medication, and more frequent visits to the doctor. Recently, researchers suggested that the effects of the nuclear accident may actually be observerd more than 30 years later by measuring the community cancer rates among individuals whose parents and grandparents were initally exposed.
You were asked to determine if there is a significant proportion of community cancer morbidity and mortality among these offspring individuals who had parents that once lived within the 100 km proximity to the facility.

In order to determine the significance of the proportion of community cancer morbidity and mortality, you must review a representative sample of hospital records to establish the proportion of community cancer morbidity and mortality. Unfortunately, many of the individuals who once lived in the 100 km proximity to the facility are now relocated, and as such hospital records are not available.

You believe however that there continues to be enough individuals in the area to provide a representative sample. The original population was ??? individuals, and the typical rate for community cancer among individuals in other studies of other areas is approximately ??? percent. Your task is to determine the significance of the proportion of community cancer morbidity and mortality among the original population. You wish to be 93% confident that you are within??? % of the true population estimate.

Click this RNG to determine the original population from which you will draw the sample.

Use this RNG to determine the typical rate for community cancer among individuals in other studies of other areas

You wish to 93% confident so re-check the alpha level from the table in the webulator, and recall that beta levels are not explicitly required in this webulator. Further you expect that the difference between your estimate of the population proportion and the TRUE estimate of the population proportion is within percent.

The data you need for this task are:

• starting population
• the estimated proportion
• the z scores for the alpha term
• the percent difference between your estimates and estimates from previous studies.

Click here to access the Webulator for sample size for a population proportion

QUESTION #3
Symptoms associated with the condition of Carpal Tunnel Syndrome (CTS) are ubiquitous among certain types of workers. The problem appears to be especially prevalent among poultry workers. A national poultry company contacted the University to request the University's assistance in assessing the problem among the workers at Provincial poultry farms. As a researcher you contacted a local microvascular surgeon to discuss the problem. She indicated that she treated about ??? individuals per year with CTS symptoms and among those individuals about ???% were diagnosed as positive for CTS.

You indicated to the surgeon that you developed a series of measures which could indicate whether or not a person would be diagnosed as positive for CTS, and that you would like to apply these measures to a sample of her patients.

In other words you would like to test her patients!

Your task is to indicate the actual sample size you will require to establish a population proportion estimate that you are 97% confident that you are within???% of the true population estimate. The true population percentage that are diagnosed as positive for CTS are

You wish to establish a population proportion estimate that you are 97% confident that you are within percent of the true population proportion.

The data you need for this task are:

• starting population
• the estimated proportion
• the z scores for the alpha term
• the percent difference between your estimates and estimates from previous studies.

Click here to access the Webulator for sample size for a population proportion

QUESTION #4
Talk of a number of individuals returning computer disks to the ABC Computer Disk Company has reached the ears of the Company's Chief Financial Officer (CFO). The problem seems to be that the disks fail to save anything after 10 uses. The CFO is angry and has ordered a complete performance evaluation of the entire current warehouse stock or "heads will roll". Your first response is, "oh well", but then realizing that you need the job to pay your tuition, especially for this course, you rethink your response.

Instead you prepare a letter to the CFO indicating that the Company need not evaluate the entire warehouse stock of ??? diskettes.

Rather, you indicate that the Company need only evaluate a representative sample of the disks in order for the Company to ship the entire stock of disks.

The CFO likes your idea. However, because ??? percent of the December shipment was returned, the CFO wanted to be 99 percent confident that the diskettes chosen for testing would be representative of the true population proportion of bad disks.

The CFO stipulated that the representative sample size should be within ??? percent of predicting the true population proportion of bad disks.

Your task is to determine how many disks should be selected at random from the warehouse and tested for storage failure.

Proportion expected

In computing the appropriate sample size you decide to use an alpha level of 0.05, and you expect that the difference between your estimate of the proportion and the TRUE estimate is within percent.

The data you need for this task are:

• the total number of disks in the warehouse
• the proportion of bad disks in previous samples
• the z scores for the alpha term - the percent confidence that the sample is representative of the true population proportion of bad disks
• the margin of error for your predicted sample size.

Click here to access the Webulator for sample size for a population proportion

QUESTION #5
Spinning classes have arrived at the University. The latest trends indicate that about ??? percent of members at health clubs join spinning classes. You are charged with the duty of organizing spinning classes, but you are not sure how many of the staff, faculty, and students, would actually sign up.

You organize a membership survey for a representative sample of the current members. You wish to be ninety percent confident that your sample size estimate is within ??? of the true population proportion.

The data you need for this task are: - the total number of Activity Complex facility members - the typical or expected proportion of individuals that join spin classes - the percent confidence that the sample is representative of the true population proportion - the margin of error for your predicted sample size.

Your task is to determine what proportion of the current Activity Complex facility membership of (which currently consists of = ) would be interested in enrolling in a spinning class.

and the expected proportion of spinners is:

You wish to compare that the difference between your estimate and that of the TRUE population estimate is within percent.

The data you need for this task are:

• Number of members from the activity complex
• the estimated proportion of members willing to join spinning
• the z scores for the alpha term
• the percent difference between your estimates and estimates from previous studies.

Click here to access the Webulator for sample size for a population proportion