Chapter 1. Two-Sample t Procedures

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 \(\sqrt{ \frac{ \sigma _{1} ^{2} }{ n_{1} } + \frac{ \sigma _{2} ^{2} }{ n_{2} } } \).

2

Try again.

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.

2

Try again.

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.

2

Try again.

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.

2

Try again.

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.

2

Try again.

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.

2

Try again.

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.

2

Try again.

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.

2

Try again.

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.

2

Try again.

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 \(\mathrm{H_{a}: \mu_{D} > \mu_{P}}\).

2

Try again.

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.

2

Try again.

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.

2

Try again.

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.

2

Try again.

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!”

2

Try again.

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.

2

Try again.

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.

2

Try again.

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.

2

Try again.

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

Try again.

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.

2

Try again.