In this project, students will design and carry out a survey, analyze the data, and graphically display the results.
The student will design and carry out a survey.
The student will analyze and graphically display the results of the survey.
As you complete each task below, check it off. Answer all questions in your summary.
| ____ Decide what data you are going to study. Examples Here are two examples, but you may NOT use them: number of M&M's per small bag, number of pencils students have in their backpacks. | |||||
| ____ Are your data discrete or continuous? How do you know? | |||||
| ____ Decide how you are going to collect the data (for instance, buy 30 bags of M&M's; collect data from the World Wide Web). | |||||
| ____ Describe your sampling technique in detail. Use cluster, stratified, systematic, or simple random (using a random number generator) sampling. Do not use convenience sampling. What method did you use? Why did you pick that method? | |||||
| ____ Conduct your survey. Your data size must be at least 30. | |||||
| ____ Summarize your data in a chart with columns showing data value, frequency, relative frequency and cumulative relative frequency. | |||||
____ Answer the following (rounded to 2 decimal places):
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| ____ What value is 2 standard deviations above the mean? | |||||
| ____ What value is 1.5 standard deviations below the mean? | |||||
| ____ Construct a histogram displaying your data. | |||||
| ____ In complete sentences, describe the shape of your graph. | |||||
| ____ Do you notice any potential outliers? If so, what values are they? Show your work in how you used the potential outlier formula in Chapter 2 (since you have univariate data) to determine whether or not the values might be outliers. | |||||
| ____ Construct a box plot displaying your data. | |||||
| ____ Does the middle 50% of the data appear to be concentrated together or spread apart? Explain how you determined this. | |||||
| ____ Looking at both the histogram and the box plot, discuss the distribution of your data. |
You need to turn in the following typed and stapled packet, with pages in the following order:
| ____ Cover sheet: name, class time, and name of your study |
| ____ Summary page: This should contain paragraphs written with complete sentences. It should include answers to all the questions above. It should also include statements describing the population under study, the sample, a parameter or parameters being studied, and the statistic or statistics produced. |
| ____ URL for data, if your data are from the World Wide Web. |
| ____ Chart of data, frequency, relative frequency and cumulative relative frequency. |
| ____ Page(s) of graphs: histogram and box plot. |
In this project, students will identify and analyze a continuous data set, determine which distribution model most closely describes the data, and calculate probabilities.
The student will collect a sample of continuous data.
The student will attempt to fit the data sample to various distribution models.
The student will validate the Central Limit Theorem.
As you complete each task below, check it off. Answer all questions in your summary.
| ____ Decide what continuous data you are going to study. (Here are two examples, but you may NOT use them: the amount of money a student spends on college supplies this term or the length of a long distance telephone call.) | ||
| ____ Describe your sampling technique in detail. Use cluster, stratified, systematic, or simple random (using a random number generator) sampling. Do not use convenience sampling. What method did you use? Why did you pick that method? | ||
| ____ Conduct your survey. Gather at least 150 pieces of continuous quantitative data. | ||
| ____ Define (in words) the random variable for your data. X = _______ | ||
| ____ Create 2 lists of your data: (1) unordered data, (2) in order of smallest to largest. | ||
____ Find the sample mean and the sample standard deviation (rounded to 2 decimal places).
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| ____ Construct a histogram of your data containing 5 - 10 intervals of equal width. The histogram should be a representative display of your data. Label and scale it. |
| ____ Suppose that X followed the theoretical distributions below. Set up each distribution using the appropriate information from your data. | ||||
| ____ Uniform: X ~ U ____________ Use the lowest and highest values as a and b. | ||||
____ Exponential: X ~ Exp ____________Use  to estimate μ . | ||||
____ Normal: X ~ N ____________ Use  to estimate for μ and s to estimate for σ. | ||||
| ____ Must your data fit one of the above distributions? Explain why or why not. | ||||
| ____ Could the data fit 2 or 3 of the above distributions (at the same time)? Explain. | ||||
____ Calculate the value k (an X value) that is 1.75 standard deviations above the sample mean.
k = _________ (rounded to 2 decimal places) Note:  | ||||
____ Determine the relative frequencies (RF) rounded to 4 decimal places.
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Use a separate piece of paper for EACH distribution (uniform, exponential, normal) to respond to the following questions.
You should have one page for the uniform, one page for the exponential, and one page for the normal
| ____ State the distribution: X ~ _________ | |||
| ____ Draw a graph for each of the three theoretical distributions. Label the axes and mark them appropriately. | |||
____ Find the following theoretical probabilities (rounded to 4 decimal places).
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| ____ Compare the relative frequencies to the corresponding probabilities. Are the values close? | |||
| ____ Does it appear that the data fit the distribution well? Justify your answer by comparing the probabilities to the relative frequencies, and the histograms to the theoretical graphs. |
| ______ From your original data (before ordering), use a random number generator to pick 40 samples of size 5. For each sample, calculate the average. | |||
| ______ On a separate page, attached to the summary, include the 40 samples of size 5, along with the 40 sample averages. | |||
| ______ List the 40 averages in order from smallest to largest. | |||
______ Define the random variable,  , in words.  = | |||
______ State the approximate theoretical distribution of  .  | |||
| ______ Base this on the mean and standard deviation from your original data. | |||
| ______ Construct a histogram displaying your data. Use 5 to 6 intervals of equal width. Label and scale it. | |||
Calculate the value  (an  value) that is 1.75 standard deviations above the sample mean.
 = _____ (rounded to 2 decimal places) | |||
Determine the relative frequencies (RF) rounded to 4 decimal places.
| |||
Find the following theoretical probabilities (rounded to 4 decimal places).
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| ______ Draw the graph of the theoretical distribution of X. | |||
| ______ Answer the questions below. | |||
| ______ Compare the relative frequencies to the probabilities. Are the values close? | |||
______ Does it appear that the data of averages fit the distribution of  well? Justify your answer
by comparing the probabilities to the relative frequencies, and the histogram to the
theoretical graph. | |||
| ______ In 3 - 5 complete sentences for each, answer the following questions. Give thoughtful explanations. | |||
| ______ In summary, do your original data seem to fit the uniform, exponential, or normal distributions? Answer why or why not for each distribution. If the data do not fit any of those distributions, explain why. | |||
| ______ What happened to the shape and distribution when you averaged your data? In theory, what should have happened? In theory, would “it” always happen? Why or why not? | |||
______ Were the relative frequencies compared to the theoretical probabilities closer when
comparing the X or  distributions? Explain your answer. |
You need to turn in the following typed and stapled packet, with pages in the following order:
| ____ Cover sheet: name, class time, and name of your study |
| ____ Summary pages: These should contain several paragraphs written with complete sentences that describe the experiment, including what you studied and your sampling technique, as well as answers to all of the questions above. |
| ____ URL for data, if your data are from the World Wide Web. |
| ____ Pages, one for each theoretical distribution, with the distribution stated, the graph, and the probability questions answered |
| ____ Pages of the data requested |
| ____ All graphs required |
In this project, students will identify real-world examples of hypothesis testing in the media. Students will then conduct their own survey and compare results.
The student will identify a hypothesis testing problem in print.
The student will conduct a survey to verify or dispute the results of the hypothesis test.
The student will summarize the article, analysis, and conclusions in a report.
As you complete each task below, check it off. Answer all questions in your summary.
| ____ Find an article in a newspaper, magazine or on the internet which makes a claim about ONE population mean or ONE population proportion. The claim may be based upon a survey that the article was reporting on. Decide whether this claim is the null or alternate hypothesis. |
| ____ Copy or print out the article and include a copy in your project, along with the source. |
| ____ State how you will collect your data. (Convenience sampling is not acceptable.) |
| ____ Conduct your survey. You must have more than 50 responses in your sample. When you hand in your final project, attach the tally sheet or the packet of questionnaires that you used to collect data. Your data must be real. |
| ____ State the statistics that are a result of your data collection: sample size, sample mean, and sample standard deviation, OR sample size and number of successes. |
| ____ Make 2 copies of the appropriate solution sheet. |
| ____ Record the hypothesis test on the solution sheet, based on your experiment. Do a DRAFT solution first on one of the solution sheets and check it over carefully. Have a classmate check your solution to see if it is done correctly. Make your decision using a 5% level of significance. Include the 95% confidence interval on the solution sheet. |
| ____ Create a graph that illustrates your data. This may be a pie or bar chart or may be a histogram or box plot, depending on the nature of your data. Produce a graph that makes sense for your data and gives useful visual information about your data. You may need to look at several types of graphs before you decide which is the most appropriate for the type of data in your project. |
| ____ Write your summary (in complete sentences and paragraphs, with proper g
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