Question

A random sample of 376 married couples found that 296 had two or more personality preferences in common. In another random sample of 586 married couples, it was found that only 20 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.)

lower limit
upper limit

Most married couples have two or three personality preferences in common. A random sample of 362 married couples found that 136 had three preferences in common. Another random sample of 552 couples showed that 214 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.

(b) Find a 99% confidence interval for p₁ – p₂. (Use 3 decimal places.)

lower limit
upper limit

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 9780 observations, the sample mean interval was x₁ = 61.4 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 24,053 observations, the sample mean time interval was x₂ = 69.4 minutes. Historical data suggest that σ₁ = 9.47 minutes and σ₂ = 11.57 minutes. Let μ₁ be the population mean of x₁ and let μ₂ be the population mean of x₂.

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

lower limit
upper limit

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 40 mothers gave a sample mean of x₁ = 68.87. Another random sample of 38 fathers gave x₂ = 60.70. Assume that σ₁ = 11.41 and σ₂ = 11.41.

(d) 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.)

lower limit
upper limit

Answer 1