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Unformatted text preview: OneSample Inference Review
Portions of Chapters 89 (ebook only) Inference Review 1 OneSample Inference During the last half of your prerequisite course (STA2023 on campus), you would have covered basic confidence interval estimates and hypothesis tests. We will review these quickly by looking at several examples. A detailed explanation of each one is on the MyStatLab site.
Inference Review 2 Confidence Intervals An interval estimate is a range of values for some population parameter, for example: 133 < < 163. The interval is derived using probability from some distribution. If, for example, . 95 probability is used, we call the result a 95% confidence interval.
Inference Review 3 Symmetric intervals Many intervals have a symmetric form and can be stated: point estimate ME Here point estimate is our "best guess" of the population parameter's value and ME is the estimator's margin of error.
Inference Review 4 Example 1: Patient Expenses Administrators at St. Regis Hospital want to know the average amount spent on medical expenses for patients admitted last year. Past studies have shown that the standard deviation per patient was about $500. From last year's admissions, a sample of 200 patients had an average expense of $5230. Use this info to make a 90% interval estimate. Inference Review 5 Interval when is known
We will use X for the sample mean and n for the sample size. Interval is: X z n ( Z is a value from the standard normal distribution.) Inference Review 6 Computations Interval: Interpretation: Inference Review 7 Using PhStat Inference Review 8 Need more help? In the ebook, this topic is covered in section 8.1. A video about the medical expense example is on the MyStatLab site. Look under "Student Videos" Inference Review 9 Example 2: Checkout Errors The CPA firm Medlin and Associates conducts an audit at a discount store to estimate the average amount of error per item at the checkout line. They want to use the information from the sample below to make a 90% interval estimate.
1.20 1.10 0.43 2.60 1.00 0.00 1.47 0.00 0.83 1.70 0.50 0.83 3.34 1.99 1.58 0.00 1.46 1.34 0.00 0.36 Inference Review 10 Interval when is not known
We will estimate from the population by S the sample standard deviation. Interval is: S X t n ( t is a value from the t distribution with n1 degrees of freedom.) Inference Review 11 Area in Upper Tail Table E.3 (pg 739) illustrated for n=20, 95% interval) df 1 2 3 : 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 0.1 3.078 1.886 1.638 : 1.341 1.337 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310 1.303 1.296 1.289 1.282 0.05 6.314 2.920 2.353 : 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.684 1.671 1.658 1.645 0.025 12.706 4.303 3.182 : 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.021 2.000 1.980 1.960 0.01 31.821 6.965 4.541 : 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.390 2.358 2.326 0.005 63.657 9.925 5.841 : 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.704 2.660 2.617 2.576 Inference Review 12 Computations Data file: CheckOutErrors.xls Interval: Interpretation:
Inference Review 13 Using CIE sigma unknown.xls
Estimate for the Mean S ales Invoice Amount Data S ample S tandard Deviation S ample Mean S ample S ize Confidence Level Intermediate Calculations S tandard Error of the Mean Degrees of Freedom t Value Interval Half Width Confidence Interval Interval Lower Limit Interval Upper Limit Come with the 28.95 110.27 100 95% 2.8950 99 1.9842 5.7443 inputs for textbook example. Change the numbers in the light blue area. 104.53 116.01
Inference Review 14 Example 3: Quick Lube A computer program tracks its customers and sends out a reminder card when it estimates they are due for another oil change. It usually has a $5 off coupon. What percentage of customers respond? For a sample of 100 customers, 62 returned to Quick Lube within one month of the mailing date. Make a 95% interval estimate for all customers. Inference Review 15 A different type of variable
Sample n observations from the population On each observation, we simply observe whether a particular characteristic is present or not. We want to estimate the proportion in the population that "have it" Inference Review 16 Estimate of = the proportion in the population having our target characteristic
The sample proportion provides an estimate X number that " Have it " p= = n sample size Inference Review 17 Interval for P
The form is: p ME
where the margin of error is: ME = Z / 2
Inference Review p (1  p ) n
18 Computations By hand On computer Inference Review 19 Example 4: Commute time The average commute in Orange County CA has been considered 40 minutes or less, with a standard deviation of 8 minutes. Researchers claim it has increased. They cite their study of 100 people, who averaged 43.5 minutes. At a 5% level of significance, is this sufficient evidence to claim an increase? Inference Review 20 Example 5: Dairy Fresh Ice Cream The halfgallon ice cream container should contain 64 ounces of product. The automatic filling machine can go out of adjustment either on the high or low side. To monitor this, the company selects a sample of 16 containers each day. The results for several days are in DairyFresh.xls. At a 5% level of significance, does this data show an adjustment is needed on day 1? Inference Review 21 Similarities How are the two examples the same? How are they different? Inference Review 22 The test statistic Has the general form: X  0 Test statistic = std . error Example 4: 0 Example 5: 0 = = std. error = std. error =
Inference Review 23 Example 4: commute time
Hypothesis Test statistic Decision rule Results
Inference Review 24 Using PhStat Inference Review 25 Results
Has commute time gone up? Data Null Hypothesis = Level of Significance Population Standard Deviation Sample Size Sample Mean Intermediate Calculations Standard Error of the Mean Z Test Statistic UpperTail Test Upper Critical Value p Value Reject the null hypothesis 40 0.05 8 100 43.5 The blue cells are now "live". What is this p 0.8000 4.3750 value stuff? How is it used? 1.6449 0.0000 Inference Review 26 Example 5: ice cream
Hypothesis Test statistic Decision rule Results
Inference Review 27 Using the T mean.xls workbook
t Test for the Hypothesis of the Mean Data = COMPUTE sheet
64 0.05 16 64.675 0.7541 Null Hypothesis Level of S ignificance S ample S ize S ample Mean S ample S tandard Deviation is for 2sided H1 COMPUTE_ LOWER is Intermediate Calculations S tandard Error of the Mean Degrees of Freedom t Test S tatistic 0.1885 15 3.5804 TwoTail Test Lower Critical Value 2.1314 Upper Critical Value 2.1314 p Value 0.0027 Reject the null hypothesis for lowertail test COMPUTE_ UPPER is for uppertail test This is Day3. Inference Review 28 ...
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 Spring '08
 Thompson

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