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## Inferential Statistics

Submit your assignment 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 | ||||||||||

#2 | #2 | ||||||||||

#3 | #3 | ||||||||||

#4 | #4 | ||||||||||

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 | ||||||||||

#6 | #6 | ||||||||||

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 | |||||||||

#2 | p | p | |||||||||

#3 | p | p | |||||||||

#4 | p | p | |||||||||

#5 | μ | μ | |||||||||

#6 | μ | μ | |||||||||

End of table, blank row. | |||||||||||

Rejection criteria: | |||||||||||

Left-tailed test (one-sided), reject Ho when z < -1.645. | |||||||||||

Right-tailed test (one-sided), reject Ho when z > 1.645. | |||||||||||

Two-tailed test (two-sided), 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 | 61 | #1 | 0.1271116716 | 0.4328883284 | 0.6871116716 | We are 95% confident the true population proportion is between 0.293 and 0.547 | ||||

#2 | 0.43 | 61 | #2 | 0.1267759092 | 0.3032240908 | 0.5567759092 | We are 95% confident the true population proportion is between 0.604 and 0.836. | ||||

#3 | 0.48 | 61 | #3 | 0.1279344094 | 0.3520655906 | 0.6079344094 | We are 95% confident the true population proportion is between 0.453 and 0.707. | ||||

#4 | 0.44 | 61 | #4 | 0.1271116716 | 0.3128883284 | 0.5671116716 | We are 95% confident the true population proportion is between 0.527 and 0.773. | ||||

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 | 3.61 | 1.43 | 61 | #5 | 0.3661854766 | 3.2438145234 | 3.9761854766 | We are 95% confident the true population mean is between 14.72 and 15.92. | |||

#6 | 492.03 | 136.62 | 61 | #6 | 34.9847970729 | 457.0452029271 | 527.0147970729 | We are 95% confident the true population mean is between 118.17 and 123.95. | |||

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 | 0.1569919254 | Reject Ho | There is sufficient statistical evidence to show the population proportion is less than 0.55. | |||||

#2 | p ≤ 0.50 | p > 0.50 | z > 1.645 | -1.0934349546 | Reject Ho | There is 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 | -5.5914696935 | 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 | -73.1323378744 | 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 | Do not Reject Ho | There is not sufficient statistical evidence to show the population mean is greater than 119. | |||||

End of table, blank row. | |||||||||||

Rejection criteria: | |||||||||||

Left-tailed test (one-sided), reject Ho when z < -1.645. | |||||||||||

Right-tailed test (one-sided), reject Ho when z > 1.645. | |||||||||||

Two-tailed test (two-sided), 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.