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December 3, 2024

Submit the Excel template containing your work. Before submitting your assessment, verify you have included all of the elements listed above. Note: Be su

Mathematics / Statistics

Submit the Excel template containing your work. Before submitting your assessment, verify you have included all of the elements listed above.

Note: Be sure to complete Assessment 3 before completing this assessment.

By completing Assessment 3, you are now in the position of having data and summary statistics for your survey. 

Use the Inferential Statistics to Analyze Data Template [XLSX] to complete this assessment. Review the "Example" sheet in the file first. Then use the corresponding information from Assessment 3 in the "Inferential Statistics" sheet of the template.

For this assessment, analyze data using inferential statistics for your previously defined survey questions. Before you begin your analysis, note the following:

  • When using the Inferential Statistics to Analyze Data Template, note that there are two pages. Be sure to review each one carefully. The first page is the blank template that you will complete, and the second page is a completed example. Try to model your results on the ones shown.
  • Enter the sample statistics (proportions and samples sizes for questions 1–4 as well as the sample means, standard deviations, and sample sizes for questions 5–6) in the respective fields of the template. The sample statistics were calculated for each survey question in Assessment 3. Use this prior work to complete this assessment. Note that the sample size must be the same for all six questions.

  1. Calculate a 95% confidence interval for each of your survey questions (1–6). Your final product should have six confidence intervals.
  2. Perform a hypothesis test for each survey question (1–6). Your final product should have six hypothesis tests.

A few notes:

  • When determining the null and alternative hypotheses for each question, use the typical response values from Assessment 2. 
  • You probably want to write the null hypothesis first. Then, the alternative hypothesis is the opposite of the alternative.
  • Use the same numerical value for the two hypotheses. You cannot put one value for the null and another for the alternative.
  • For questions 1–4, we are using the sample proportion to estimate the population proportion. For questions 5–6, we are using the sample mean to estimate the population mean. Thus, we use different formulas for their confidence intervals and for their test statistics in the hypothesis tests.

By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies and rubric criteria:

  • Competency 3: Derive logical conclusions from inferential statistical procedures.
    • Compute 95% confidence intervals correctly for multiple variables in a study.
    • Derive appropriate conclusions based upon calculated confidence intervals for a study.
    • Choose appropriate hypothesis tests based upon the context of the questions asked.
    • Specify correct null and alternative hypotheses.
    • Calculate hypothesis tests correctly for multiple questions in a study.
    • Derive appropriate conclusions regarding hypotheses according to the results of hypothesis tests.
  • attachment

    cf_inferential_statistics_data_template.xlsx

  • attachment

    Assessment3–MAT-FPX2001-.xlsx

Inferential Statistics

Your assessment must be submitted using this template. Feel free to add additional work at the bottom, but the top must remain.
There are five tables in this worksheet: two for statistical summary, two for confidence intervals, and one for hypothesis tests.
To find a table quickly, press Ctrl+G. Press the Tab key to move to input areas of the table.
Note: See the worksheet named "Example" (in the bottom tab) for examples of how to fill in the yellow boxes.
Blank row, Table 1 begins in A8.
Blank row, Table 1 begins in A8.
Statistical Summary: Questions 1–4 Confidence Intervals: Questions 1–4
Question Sample Proportion Sample Size Question Error Lower Limit Upper Limit Conclusion
#1 #1 ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0!
#2 #2 ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0!
#3 #3 ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0!
#4 #4 ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0!
End of Table 1, blank row. Table 2 begins in F8. End of Table 2, blank row. Table 3 begins in A15.
Statistical Summary: Questions 5–6 Confidence Intervals: Questions 5–6
Question Sample Mean Sample Std Dev Sample Size Question Error Lower Limit Upper Limit Conclusion
#5 #5 ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0!
#6 #6 ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0!
End of Table 3, blank row. Table 4 begins in F15. End of table, blank row. Table 5 begins in F21.
Blank row. Table 4 begins in F15. End of table, blank row. Table 5 begins in F21.
Table 5 begins in F21. Hypothesis Tests: Questions 1–6
Question Ho Ha Reject Ho When Test Statistic Decision Summary
#1 p p ERROR:#DIV/0!
#2 p p ERROR:#DIV/0!
#3 p p ERROR:#DIV/0!
#4 p p ERROR:#DIV/0!
#5 μ μ ERROR:#DIV/0!
#6 μ μ ERROR:#DIV/0!
End of table, blank row.
Rejection criteria:
Left-tailed test, reject Ho when z < -1.645.
Right-tailed test, reject Ho when z > 1.645.
Two-tailed test, reject Ho when z < -1.96 or z > 1.96.
End of worksheet.

IMPORTANT: Be sure you change the population statistic in the Test Statistic formula to reflect what you put in Ho and Ha.

Example

The work below uses made-up data. Remember that the values you use in your hypotheses are up to you.
You can compare your population parameters to any value; just remember that the sample statistic must agree with your alternate hypothesis.
We always try to reject the null hypothesis; that means we must have evidence (via the sample statistic) that the alternate hypothesis is true.
Click in the cell to see the formula used.
Blank row, Table 1 begins in A8.
Blank row, Table 1 begins in A8.
Statistical Summary: Questions 1–4 Confidence Intervals: Questions 1–4
Question Sample Proportion Sample Size Question Error Lower Limit Upper Limit Conclusion
#1 0.56 322 #1 0.055325126 0.504674874 0.615325126 We are 95% confident the true population proportion is between 0.505 and 0.615.
#2 0.43 322 #2 0.055178986 0.374821014 0.485178986 We are 95% confident the true population proportion is between 0.375 and 0.485.
#3 0.48 61 #3 0.1279344094 0.3520655906 0.6079344094 We are 95% confident the true population proportion is between 0.352 and 0.608.
#4 0.852 61 #4 0.0909317885 0.7610682115 0.9429317885 We are 95% confident the true population proportion is between 0.761 and 0.943.
End of Table 1, blank row. Table 2 begins in F8. End of Table 2, blank row. Table 3 begins in A15.
Statistical Summary: Questions 5–6 Confidence Intervals: Questions 5–6
Question Sample Mean Sample Std Dev Sample Size Question Error Lower Limit Upper Limit Conclusion
#5 18.7 1.5 322 #5 0.1671834638 18.5328165362 18.8671834638 We are 95% confident the true population proportion is between 18.533 and 18.867.
#6 492.03 136.62 61 #6 34.9847970729 457.0452029271 527.0147970729 We are 95% confident the true population proportion is between 457.045 and 527.015.
End of Table 3, blank row. Table 4 begins in F15. End of table, blank row. Table 5 begins in F21.
Blank row. Table 4 begins in F15. End of table, blank row. Table 5 begins in F21.
Table 5 begins in F21. Hypothesis Tests: Questions 1–6
Question Ho Ha Reject Ho When Test Statistic Decision Summary
#1 p ≥ 0.55 p < 0.55 z < -1.645 2.1533230134 Do not Reject Ho There is not sufficient statistical evidence to show the population proportion is less than 0.55.
#2 p ≤ 0.50 p > 0.50 z > 1.645 3.009727818 Do not Reject Ho There is not sufficient statistical evidence to show the population proportion is greater than 0.50.
#3 p = 0.60 p ≠ 0.60 z < -1.96 or z > 1.96 -1.913112647 Do not Reject Ho There is not sufficient statistical evidence to show the populaton proportion is not 0.60.
#4 p ≥ 0.75 p < 0.75 z < -1.645 1.8397738992 Reject Ho There is sufficient statistical evidence to show the population proportion is less than 0.75.
#5 μ = 17 μ ≠ 17 z < -1.96 or z > 1.96 8.374033941 Reject Ho There is sufficient statistical evidence to show the population mean is not 17.
#6 μ ≤ 119 μ > 119 z > 1.645 21.3252630406 Reject Ho There is sufficient statistical evidence to show the population mean is greater than 119.
End of table, blank row.
Rejection criteria:
Left-tailed test, reject Ho when z < -1.645.
Right-tailed test, reject Ho when z > 1.645.
Two-tailed test, reject Ho when z < -1.96 or z > 1.96.
End of worksheet.

IMPORTANT: Be sure you change the population statistic in the Test Statistic formula to reflect what you put in Ho and Ha.

Remember that the values used in the hypotheses are whatever you want; just make sure the sample statistic supports Ha.

FORMAT HINT: Copy the math notation to another cell using copy, then paste. Right-click in the cell to see these options.

,

data analysis

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Q1 Q2 Q3 Q4 Q5 Q6 Sarah Levin
0 0 1 1 6 2
1 1 1 0 7 4 Q5 Q6
0 1 1 1 7 5
0 1 1 1 8 2 Mean 4.7142857143 Mean 3.369047619
0 1 1 0 7 6 Standard Error 0.2071384058 Standard Error 0.1884348083
0 1 1 1 8 4 Median 5 Median 4
0 0 0 1 4 2 Mode 3 Mode 4
0 0 1 0 6 4 Standard Deviation 1.8984548478 Standard Deviation 1.7270335449
0 1 0 0 6 1 Sample Variance 3.604130809 Sample Variance 2.9826448652
1 1 0 0 4 3 Kurtosis -0.3187497928 Kurtosis -0.2278284355
1 0 1 0 6 5 Skewness 0.1738266765 Skewness 0.0687509261
0 1 0 1 3 4 Range 9 Range