10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances...
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![Page 1: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/1.jpg)
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10-1 Introduction
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10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
Figure 10-1 Two independent populations.
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10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
Assumptions
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10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
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10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
10-2.1 Hypothesis Tests for a Difference in Means, Variances Known
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10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
Example 10-1
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10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
Example 10-1
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10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
Example 10-1
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10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
10-2.2 Choice of Sample Size
Use of Operating Characteristic Curves
Two-sided alternative:
One-sided alternative:
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10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
10-2.2 Choice of Sample Size
Sample Size Formulas
Two-sided alternative:
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10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
10-2.2 Choice of Sample Size
Sample Size Formulas
One-sided alternative:
![Page 15: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/15.jpg)
10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
Example 10-3
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10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
10-2.3 Identifying Cause and Effect
• When statistical significance is observed in a randomized experiment, the experimenter can be confident in the conclusion that it was the difference in treatments that resulted in the difference in response.
• That is, we can be confident that a cause-and-effect relationship has been found.
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10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
10-2.4 Confidence Interval on a Difference in Means, Variances Known
Definition
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10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
Example 10-4
![Page 19: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/19.jpg)
10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
Example 10-4
![Page 20: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/20.jpg)
10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
Choice of Sample Size
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10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known
One-Sided Confidence Bounds
Upper Confidence Bound
Lower Confidence Bound
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10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown
10-3.1 Hypotheses Tests for a Difference in Means, Variances Unknown
We wish to test:
Case 1: 22
221
![Page 23: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/23.jpg)
10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown
10-3.1 Hypotheses Tests for a Difference in Means, Variances Unknown
The pooled estimator of 2:
Case 1: 222
21
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10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown
10-3.1 Hypotheses Tests for a Difference in Means, Variances Unknown
Case 1: 222
21
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10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown
Definition: The Two-Sample or Pooled t-Test*
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10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown
Example 10-5
![Page 27: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/27.jpg)
10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown
Example 10-5
![Page 28: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/28.jpg)
10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown
Example 10-5
![Page 29: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/29.jpg)
10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown
Example 10-5
![Page 30: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/30.jpg)
10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown
Minitab Output for Example 10-5
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Figure 10-2 Normal probability plot and comparative box plot for the catalyst yield data in Example 10-5. (a) Normal probability plot, (b) Box plots.
![Page 32: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/32.jpg)
10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown10-3.1 Hypotheses Tests for a Difference in Means, Variances Unknown
22
21 Case 2:
is distributed approximately as t with degrees of freedom given by
![Page 33: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/33.jpg)
10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown10-3.1 Hypotheses Tests for a Difference in Means, Variances Unknown
22
21 Case 2:
![Page 34: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/34.jpg)
10-3 Inference for a Difference in Means of Two Normal Distributions, Variances UnknownExample 10-6
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Example 10-6
Figure 10-3 Normal probability plot of the arsenic concentration data from Example 10-6.
![Page 36: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/36.jpg)
Example 10-6
![Page 37: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/37.jpg)
Example 10-6
![Page 38: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/38.jpg)
10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown
10-3.3 Choice of Sample Size
Two-sided alternative:
![Page 39: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/39.jpg)
10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown
Example 10-7
![Page 40: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/40.jpg)
10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown
Minitab Output for Example 10-7
![Page 41: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/41.jpg)
10-3.4 Confidence Interval on the Difference in Means
Case 1:
222
21
![Page 42: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/42.jpg)
10-3.4 Confidence Interval on the Difference in Means
Case 1:
222
21
Example 10-8
![Page 43: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/43.jpg)
10-3.4 Confidence Interval on the Difference in Means
Case 1:
222
21
Example 10-8
![Page 44: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/44.jpg)
10-3.4 Confidence Interval on the Difference in Means
Case 1:
222
21
Example 10-8
![Page 45: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/45.jpg)
10-3.4 Confidence Interval on the Difference in Means
Case 1:
222
21
Example 10-8
![Page 46: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/46.jpg)
10-3.4 Confidence Interval on the Difference in Means
Case 2:
Definition
22
21
![Page 47: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/47.jpg)
• A special case of the two-sample t-tests of Section 10-3 occurs when the observations on the two populations of interest are collected in pairs.
• Each pair of observations, say (X1j , X2j ), is taken under homogeneous conditions, but these conditions may change from one pair to another.
• The test procedure consists of analyzing the differences between hardness readings on each specimen.
10-4 Paired t-Test
![Page 48: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/48.jpg)
The Paired t-Test
10-4 Paired t-Test
![Page 49: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/49.jpg)
Example 10-9
10-4 Paired t-Test
![Page 50: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/50.jpg)
Example 10-9
10-4 Paired t-Test
![Page 51: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/51.jpg)
Example 10-9
10-4 Paired t-Test
![Page 52: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/52.jpg)
Paired Versus Unpaired Comparisons
10-4 Paired t-Test
![Page 53: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/53.jpg)
A Confidence Interval for D
10-4 Paired t-Test
Definition
![Page 54: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/54.jpg)
Example 10-10
10-4 Paired t-Test
![Page 55: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/55.jpg)
Example 10-10
10-4 Paired t-Test
![Page 56: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/56.jpg)
10-5.1 The F Distribution
10-5 Inferences on the Variances of Two Normal Populations
We wish to test the hypotheses:
• The development of a test procedure for these hypotheses requires a new probability distribution, the F distribution.
![Page 57: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/57.jpg)
10-5.1 The F Distribution
10-5 Inferences on the Variances of Two Normal Populations
![Page 58: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/58.jpg)
10-5.1 The F Distribution
10-5 Inferences on the Variances of Two Normal Populations
![Page 59: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/59.jpg)
10-5.1 The F Distribution
10-5 Inferences on the Variances of Two Normal Populations
The lower-tail percentage points f-1,u, can be found as follows.
![Page 60: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/60.jpg)
10-5.3 Hypothesis Tests on the Ratio of Two Variances
10-5 Inferences on the Variances of Two Normal Populations
![Page 61: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/61.jpg)
10-5.3 Hypothesis Tests on the Ratio of Two Variances
10-5 Inferences on the Variances of Two Normal Populations
![Page 62: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/62.jpg)
Example 10-11
10-5 Inferences on the Variances of Two Normal Populations
![Page 63: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/63.jpg)
Example 10-11
10-5 Inferences on the Variances of Two Normal Populations
![Page 64: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/64.jpg)
Example 10-11
10-5 Inferences on the Variances of Two Normal Populations
![Page 65: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/65.jpg)
10-5.4 -Error and Choice of Sample Size
10-5 Inferences on the Variances of Two Normal Populations
![Page 66: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/66.jpg)
Example 10-12
10-5 Inferences on the Variances of Two Normal Populations
![Page 67: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/67.jpg)
10-5.5 Confidence Interval on the Ratio of Two Variances
10-5 Inferences on the Variances of Two Normal Populations
![Page 68: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/68.jpg)
Example 10-13
10-5 Inferences on the Variances of Two Normal Populations
![Page 69: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/69.jpg)
Example 10-13
10-5 Inferences on the Variances of Two Normal Populations
![Page 70: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/70.jpg)
Example 10-13
10-5 Inferences on the Variances of Two Normal Populations
![Page 71: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/71.jpg)
10-6.1 Large-Sample Test for H0: p1 = p2
10-6 Inference on Two Population Proportions
We wish to test the hypotheses:
![Page 72: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/72.jpg)
10-6.1 Large-Sample Test for H0: p1 = p2
10-6 Inference on Two Population Proportions
The following test statistic is distributed approximately as standard normal and is the basis of the test:
![Page 73: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/73.jpg)
10-6.1 Large-Sample Test for H0: p1 = p2
10-6 Inference on Two Population Proportions
![Page 74: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/74.jpg)
Example 10-14
10-6 Inference on Two Population Proportions
![Page 75: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/75.jpg)
Example 10-14
10-6 Inference on Two Population Proportions
![Page 76: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/76.jpg)
Example 10-14
10-6 Inference on Two Population Proportions
![Page 77: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/77.jpg)
Minitab Output for Example 10-14
10-6 Inference on Two Population Proportions
![Page 78: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/78.jpg)
10-6.3 -Error and Choice of Sample Size
10-6 Inference on Two Population Proportions
![Page 79: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/79.jpg)
10-6.3 -Error and Choice of Sample Size
10-6 Inference on Two Population Proportions
![Page 80: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/80.jpg)
10-6.3 -Error and Choice of Sample Size
10-6 Inference on Two Population Proportions
![Page 81: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/81.jpg)
10-6.4 Confidence Interval for p1 – p2
10-6 Inference on Two Population Proportions
![Page 82: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/82.jpg)
Example 10-15
10-6 Inference on Two Population Proportions
![Page 83: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/83.jpg)
Example 10-15
10-6 Inference on Two Population Proportions
![Page 84: 10-1 Introduction 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d3f5503460f94a180ad/html5/thumbnails/84.jpg)