Question

Practice Study Guide Questions

1) Independent random samples of professional football and basketball players gave the following information. Assume that the weight distributions are mound-shaped and symmetric.

Weights (in lb) of pro football players: x₁; n₁ = 21

245	263	254	251	244	276	240	265	257	252	282
256	250	264	270	275	245	275	253	265	271

Weights (in lb) of pro basketball players: x₂; n₂ = 19

205	200	220	210	191	215	222	216	228	207
225	208	195	191	207	196	183	193	201

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to one decimal place.)

x1 =
s1 =
x2 =
s2 =

(b) Let μ₁ be the population mean for x₁ and let μ₂ be the population mean for x₂. Find a 99% confidence interval for μ₁ − μ₂. (Round your answers to one decimal place.)

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2) The following data represent petal lengths (in cm) for independent random samples of two species of Iris.

Petal length (in cm) of Iris virginica: x₁; n₁ = 35

5.3	5.5	6.2	6.1	5.1	5.5	5.3	5.5	6.9	5.0	4.9	6.0	4.8	6.1	5.6	5.1
5.6	4.8	5.4	5.1	5.1	5.9	5.2	5.7	5.4	4.5	6.4	5.3	5.5	6.7	5.7	4.9
4.8	5.7	5.1

Petal length (in cm) of Iris setosa: x₂; n₂ = 38

1.4	1.7	1.4	1.5	1.5	1.6	1.4	1.1	1.2	1.4	1.7	1.0	1.7	1.9	1.6	1.4
1.5	1.4	1.2	1.3	1.5	1.3	1.6	1.9	1.4	1.6	1.5	1.4	1.6	1.2	1.9	1.5
1.6	1.4	1.3	1.7	1.5	1.6

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to two decimal places.)

x1 =
s1 =
x2 =
s2 =

(b) Let μ₁ be the population mean for x₁ and let μ₂ be the population mean for x₂. Find a 99% confidence interval for μ₁ − μ₂. (Round your answers to two decimal places.)

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3) A random sample of 364 married couples found that 300 had two or more personality preferences in common. In another random sample of 552 married couples, it was found that only 24 had no preferences in common. Let p₁ be the population proportion of all married couples who have two or more personality preferences in common. Let p₂ be the population proportion of all married couples who have no personality preferences in common.

(a) Find a 95% confidence interval for p₁ – p₂. (Use 3 decimal places.)

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(b) Explain the meaning of the confidence interval in part (a) in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you (at the 95% confidence level) about the proportion of married couples with two or more personality preferences in common compared with the proportion of married couples sharing no personality preferences in common?

- We can not make any conclusions using this confidence interval.

- Because the interval contains only positive numbers, we can say that a higher proportion of married couples have two or more personality preferences in common.

- Because the interval contains both positive and negative numbers, we can not say that a higher proportion of married couples have two or more personality preferences in common.

- Because the interval contains only negative numbers, we can say that a higher proportion of married couples have no personality preferences in common.

4) The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x₁ be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9740 observations, the sample mean interval was x₁ = 63.2 minutes. Let x₂ be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 25,925 observations, the sample mean time interval was x₂ = 72.0 minutes. Historical data suggest that σ₁ = 9.12 minutes and σ₂ = 12.69 minutes. Let μ₁ be the population mean of x₁ and let μ₂ be the population mean of x₂.

(a) Compute a 99% confidence interval for μ₁ – μ₂. (Use 2 decimal places.)

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5) A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x₁ be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x₂ be the empathy score of a father. A random sample of 29 mothers gave a sample mean of x₁ = 68.02. Another random sample of 26 fathers gave x₂ = 61.89. Assume that σ₁ = 10.64 and σ₂ = 10.57.

(a) Let μ₁ be the population mean of x₁ and let μ₂ be the population mean of x₂. Find a 99% confidence interval for μ₁ – μ₂. (Use 2 decimal places.)

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6) At Community Hospital, the burn center is experimenting with a new plasma compress treatment. A random sample of n₁ = 312 patients with minor burns received the plasma compress treatment. Of these patients, it was found that 258 had no visible scars after treatment. Another random sample of n₂ = 432 patients with minor burns received no plasma compress treatment. For this group, it was found that 103 had no visible scars after treatment. Let p₁ be the population proportion of all patients with minor burns receiving the plasma compress treatment who have no visible scars. Let p₂ be the population proportion of all patients with minor burns not receiving the plasma compress treatment who have no visible scars.

(a) Find a 90% confidence interval for p₁ − p₂. (Round your answers to three decimal places.)

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7) In the Focus Problem at the beginning of this chapter, a study was described comparing the hatch ratios of wood duck nesting boxes. Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 485 eggs in group I boxes, of which a field count showed about 264 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 786 eggs in group II boxes, of which a field count showed about 274 hatched.

(a) Find a point estimate p̂₁ for p₁, the proportion of eggs that hatch in group I nest box placements. (Round your answer to three decimal places.)
p̂₁ = ________

Find a 90% confidence interval for p₁. (Round your answers to three decimal places.)

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(b) Find a point estimate p̂₂ for p₂, the proportion of eggs that hatch in group II nest box placements. (Round your answer to three decimal places.)
p̂₂ = ________

Find a 90% confidence interval for p₂. (Round your answers to three decimal places.)

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(c) Find a 90% confidence interval for p₁ − p₂. (Round your answers to three decimal places.)

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8) Most married couples have two or three personality preferences in common. A random sample of 374 married couples found that 130 had three preferences in common. Another random sample of 564 couples showed that 230 had two personality preferences in common. Let p₁ be the population proportion of all married couples who have three personality preferences in common. Let p₂ be the population proportion of all married couples who have two personality preferences in common.

(a) Find a 90% confidence interval for p₁ – p₂. (Use 3 decimal places.)

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9) On the Navajo Reservation, a random sample of 230 permanent dwellings in the Fort Defiance region showed that 64 were traditional Navajo hogans. In the Indian Wells region, a random sample of 145 permanent dwellings showed that 25 were traditional hogans. Let p₁ be the population proportion of all traditional hogans in the Fort Defiance region, and let p₂ be the population proportion of all traditional hogans in the Indian Wells region.

(a) Find a 90% confidence interval for p₁ – p₂. (Use 3 decimal places.)

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Answer 1

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