Inferential Statistics to Analyze Data

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.