Statistic 200

Student	N	x̅	Ps		Student	N	x̅n	Ps
Acopan	40	50	0.22		Harris	60	30	0.40
Ambol	42	52	0.18		Jacobs	62	32	0.38
Anderson	44	54	0.22		Johnson	64	34	0.36
Attai	46	56	0.24		Kurata	66	36	0.34
Broseker	48	58	0.26		Mendoza	68	38	0.32
Buchheit	50	60	0.28		Monyei	70	40	0.26
Bullock	52	62	0.30		Munshi	72	42	0.24
Caywood	54	64	0.32		Pickering	74	44	0.42
Cox-Martinez	56	66	0.34		Rager	76	46	0.44
Eickhoff	58	68	0.36		Ritchey	78	48	0.46
Fox	80	50	0.35		Rosen	86	42	0.20
Gray	82	48	0.25		Sekamwa	88	36	0.22
Hampton	84	44	0.15		Turner	90	46	0.30

Question 1. How size of the sample affects the size of Confidence Interval?

Problem 2. Compute the 90% confidence interval for population mean based on the following sample of seven: 10, 13, 14, 16, 17, 20, 22.

Problem 3. A sample has N numbers. The mean of your sample is x̅. Take value of N and x̅ from the table above. Case A: You know the standard deviation of the population is σ=10.

What is the 95% confidence interval on the population mean? Tip: use z-factor from the Normal Distribution Table.

Case B: Now assume that you do not know the population standard deviation, but the standard deviation of sample is given, s=20. Find the 90% confidence interval for the population mean? Tip: use t-factor from the t-Distribution Table.

Problem 4. An average waiting time in some Emergency Room for N randomly selected patients is x̅ minutes (sample mean). Take value of N and x̅ from the table above.

Find Margin of Error and Confidence Interval for the population mean of waiting time in that hospital. Population standard deviation is given, σ=15 min, and Confidence Level is 99%.

Problem 5. In a poll of N people sample proportion is ps (value of N and ps is given in the Table above). Compute a 95% confidence interval for the population proportion.

Problem 6. Write any 5-8 numbers between 1 and 40. They will represent sample data. Calculate Sample Mean (x) and Sample Standard Deviation (s). We don't know the value of population mean because we don't have data for the whole population. But using this week study material we can predict interval that holds population mean:   x - is calculated sample mean, E is a Margin of Error. This is the case when we don't know population standard deviation (case 2), but we have calculated sample standard deviation (s). Here is the formula for Margin of Error: n - sample size (5,6,7,or 8). ta/2 is not ta divided by 2, it's just t-value from the given Table A-3. To calculate Margin of Error (E) we have to use Appendix Table A-3  for t-Distribution (Table A-3. t-Distribution)  The Degree of Freedom in this table is (n-1), sample size minus one. We will create the interval with 90% confidence (0.90). Significance Level α = 1 - Conf.Level = 1 - 0.90 = 0.10 On Bell-shaped curve, it will leave 10% of the area in two tails outside confidence zone. That means, in attached t-Table you should use the column with Area in Two Tails equal 0.10. So, here are your steps: 1) Write 5-8 numbers between 1 and 40; this will be your sample data. 2) Calculate sample mean (x) and sample standard deviation (s). 3) Use Appendix Table A-3. t-Distribution to find t-value. 4) Calculate Margin of Error (E) using the formula above. 5) Write Confidence Interval for Population Mean: μ= x ± E

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