# Chapter 1. Two-Sample t Procedures

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1:35

### Question 1.1

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Correct. If σ1 and σ2 were known, then $$\overline{x}$$1 – $$\overline{x}$$2 would have a Normal distribution with mean µ1 – µ2 and standard deviation $$\sqrt{ \frac{ \sigma _{1} ^{2} }{ n_{1} } + \frac{ \sigma _{2} ^{2} }{ n_{2} } }$$.
Incorrect. Correct. If σ1 and σ2 were known, then $$\overline{x}$$1 – $$\overline{x}$$2 would have a Normal distribution with mean µ1 – µ2 and standard deviation $$\sqrt{ \frac{ \sigma _{1} ^{2} }{ n_{1} } + \frac{ \sigma _{2} ^{2} }{ n_{2} } }$$.
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1:51

### Question 1.2

Correct. Just as with a one-sample t, we use s to estimate σ. Specifically, we use s1 to estimate σ1 and s2 to estimate σ2.
Incorrect. Just as with a one-sample t, we use s to estimate σ. Specifically, we use s1 to estimate σ1 and s2 to estimate σ2.
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2:36

### Question 1.3

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Correct. Using software and the approximate two-sample t option is the best option for degrees of freedom as those degrees of freedom are higher than for the conservative two-sample t.
Incorrect. Using software and the approximate two-sample t option is the best option for degrees of freedom as those degrees of freedom are higher than for the conservative two-sample t.
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3:04

### Question 1.4

Correct. H0: µ1 – µ2 = 0 which is equivalent to H0: µ1 = µ2 is a statement of zero difference or no difference.
Incorrect. H0: µ1 – µ2 = 0 which is equivalent to H0: µ1 = µ2 is a statement of zero difference or no difference.
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4:25

### Question 1.5

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Correct. H0: µ1 = µ2 is equivalent to H0: µ1 – µ2 = 0, so the value used for µ1 – µ2 is zero.
Incorrect. H0: µ1 = µ2 is equivalent to H0: µ1 – µ2 = 0, so the value used for µ1 – µ2 is zero.
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5:56

### Question 1.6

Qo2yVWlfMUdlSJ6zjPM+g2+TktEnDxVb1qmLQKpEitbwdUf5TeYv6Y09JtgP0y080faWsBpdl/uq4MxKgsspKuFoGDL2Vr1bOQOWyAaOxxpLzYa6bImWIs/gZ64Ng3hnBZ5t0DBUjFgXQBCV/D/kfuZAGrqWqdRibccXpaszOOz82bXZK5IBh03aJgiFhm/EWU6+oRexNANs6jSOdG0tF05DvxU4i88tUrMmnauJCWFhTjbXhFGR3mcv08hDcPLhzozatzidWeqFf/jJ1WchLw4Xc/RDJAIgUVEnfXYalS/KFsdr
Correct. We use $$\overline{x} _{1}$$ - $$\overline{x} _{2}$$ as a point estimate of µ1 – µ2.
Incorrect. We use $$\overline{x} _{1}$$ - $$\overline{x} _{2}$$ as a point estimate of µ1 – µ2.
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6:52

### Question 1.7

ef8T8h52NAE91iDVFewwq7LRMF1fK8Yqj3PMhn6M8hEAxBIR23s7Dnjd/FaEbiMKGWt0gJM1dfrYv+1VzTUYjAKMXdX3T527WoeOdLjVrsvhQ6xM+u9x+gfJ52UQWzIU/rjFV2MX6Skyzo4Ti9G3BeBcCdeepSHqLMViuy9awZbf1wJfXfG/849C8JCg5gMZ2eGGl/8sYxJ5DLFDEZyqvAR04xfzWVP9WmUSPD4bulqdpQa1nu2iTiWJFwsrntLmZVzJn17E3Bvu+y/11U5yOUxrvG8RGeHDwXeU9cJwW+YgU+Bft/vegje8JbfBgqDH29/vfzJO8GxNNhoHDUypDDWtZ8Uke0klUj/ft1tOCM9HtjANhrG/GrpVcmUgACI14g1lAi7ObxhnJnPj
Correct. Since the formula begins with “t =”, we use the t table to find P-value.
Incorrect. Since the formula begins with “t =”, we use the t table to find P-value.
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7:10

### Question 1.8

liDFCdre8twAPGVbg93Em47wTLhI/tZX5i8lNIBK2ZNZOXH5NQcKqpRAw9QSUu0hF/5GeNjejV+ktu8AgEv5UC2EdUyUTTLi2Mo7O9RpA9FLBLa3BudU5QA7UonSc7Y4riKpyaPREEamOnPRyQCujsEK6iGZTWs5Byrboshg5a1c+COo1uXR8sjhNRDsYBtkuzCrJONjiVn0GHNQHWu2QDVHyIHKf1V66jbMu1zBRhFtUYDfwwRgPoLbvUHHCaW1HLwKMrMhsYyOts9dKsUrmr1eAcVPjmiANY5Hl+i3HxSWqo1dTJ2Y3YWzVV+ae65gxNQTppMSp5Vh1WsB6ibMbMdhL/OUq2HdAlyLIRTnVlh9bTFK9TFQjjL1+I4vtaKVPWNOimQ06AvjTAcIrG2/gQ==
Correct. Since the formula includes “t*," we use the t table to find the multiplier.
Incorrect. Since the formula includes “t*," we use the t table to find the multiplier.
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8:54

### Question 1.9

ox0eR8HoN54P9dR/f+3XKFn9UKfBG7cKZ/YtroRHBGIumJ2YVYZ+tw9wtL8bBCHExnXeYU8M8RgL5yCpiL9Pr3Paevl+X2pI/pydch8YeckKbIJFd4OicLo95H+Uca/xENe+V1nL9LP0kBXUa03jMwq8cuT47YMTzOliaOHBivfAmVENWH7GvtjO+aZ2Z8O1XcwzpkirfhWP0ge+w3auv+EjSDvIeXxKVwDb8aFXH8ZXLGqdmHvOpoI0xWnUyiY95d4KlnwOEjkf2vjN+4HNoF4DYDh6pW/a14i5suKzWSdw82rYaVpX2dG8eHMNkJHRGyKsaTCm3533rX5AOpneT2o7xj6RRLJuShK63vgPhUsTY4bEWi/62NavjeKkNpkHP1Q6xZ92uTivTJfgo727nErnVHFSVqp+ppqcyYrGiqWiq5OZd0yIOQjLmVGJ7V6PWhccyWdurLEiuCeECKsKa+tJQTgYmF201xBKvGRUs925DyMP
Correct. We can apply the Central Limit Theorem whenever the combined sample size is large and data are collected appropriately.
Incorrect. We can apply the Central Limit Theorem whenever the combined sample size is large and data are collected appropriately.
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9:29

### Question 1.10

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
Correct. If we want to show that the mean water intake of rats receiving the drug is greater than the mean water intake of rats receiving the placebo, then we want $$\mathrm{H_{a}: \mu_{D} > \mu_{P}}$$.
Incorrect. If we want to show that the mean water intake of rats receiving the drug is greater than the mean water intake of rats receiving the placebo, then we want $$\mathrm{H_{a}: \mu_{D} > \mu_{P}}$$.
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10:41

### Question 1.11

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Correct. When we have two separate sets of quantitative data, we compare two means. In this case, the response variable is water intake which is quantitative and we have a data set for the drug group of rats and a data set for the placebo group of rats. We don’t have two populations of rats for this example.
Incorrect.When we have two separate sets of quantitative data, we compare two means. In this case, the response variable is water intake which is quantitative and we have a data set for the drug group of rats and a data set for the placebo group of rats. We don’t have two populations of rats for this example.
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10:50

### Question 1.12

Correct. Since this is an experiment, the rats should be assigned to treatments with random allocation.
Incorrect. Since this is an experiment, the rats should be assigned to treatments with random allocation.
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11:13

### Question 1.13

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Correct. Water intake was measured on each rat; this is the response variable.
Incorrect. Water intake was measured on each rat; this is the response variable.
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11:25

### Question 1.14

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Correct. We observe no observation for which you might say, “Oh, wow!!! That’s an outlier!”
Incorrect. We observe no observation for which you might say, “Oh, wow!!! That’s an outlier!”
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12:08

### Question 1.15

Correct. n1 – 1 = 10 – 1 = 9 and n2 – 1 = 10 – 1 = 9 so df = 9.
Incorrect. n1 – 1 = 10 – 1 = 9 and n2 – 1 = 10 – 1 = 9 so df = 9.
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13:08

### Question 1.16

Correct. 0.025 < P-value < 0.05 is less than α = 0.05 so we reject H0.
Incorrect. 0.025 < P-value < 0.05 is less than α = 0.05 so we reject H0.
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13:18

### Question 1.17

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Correct. Because this was a valid experiment, we can conclude that the drug caused an increase in water intake.
Incorrect. Because this was a valid experiment, we can conclude that the drug caused an increase in water intake.
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14:43

### Question 1.18

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Correct. µ1 – µ2 is the difference between the two treatment means. In this example, it is the difference between the mean water intake of rats receiving the anti-depressant drug and the mean water intake of rats receiving a placebo.
Incorrect. µ1 – µ2 is the difference between the two treatment means. In this example, it is the difference between the mean water intake of rats receiving the anti-depressant drug and the mean water intake of rats receiving a placebo.
2
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14:50

### Question 1.19

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Correct. Since the interval does not include the value of zero, we can say that µ1 – µ2 does not equal zero.
Incorrect. Since the interval does not include the value of zero, we can say that µ1 – µ2 does not equal zero.
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