A random sample of382married couples found that292had two or more personality preferences in common. In another random sample of574married couples, it was found that only22had no preferences in common. Letp₁be the population proportion of all married couples who have two or more personality preferences in common. Letp₂be the population proportion of all married couples who have no personality preferences in common.

(a) Find a90%confidence interval forp₁-p₂. (Use 3 decimal places.)

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Most married couples have two or three personality preferences in common. A random sample of370married couples found that124had three preferences in common. Another random sample of580couples showed that226had two personality preferences in common. Letp₁be the population proportion of all married couples who have three personality preferences in common. Letp₂be the population proportion of all married couples who have two personality preferences in common.

(a) Find a95%confidence interval forp₁-p₂. (Use 3 decimal places.)

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The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Letx₁be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on9180observations, the sample mean interval wasx₁=65.0minutes. Letx₂be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on24,170observations, the sample mean time interval wasx₂=70.8minutes. Historical data suggest that₁=8.77minutes and₂=11.50minutes. Let₁be the population mean ofx₁and let₂be the population mean ofx₂.

(a) Compute a95%confidence interval for₁-₂. (Use 2 decimal places.)

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A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Letx₁be a random variable that represents the score of a mother on an empathy test (as regards her baby). Letx₂be the empathy score of a father. A random sample of40mothers gave a sample mean ofx₁=69.72. Another random sample of40fathers gavex₂=57.68. Assume that₁=11.41and₂=11.32.

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Let₁be the population mean ofx₁and let₂be the population mean ofx₂. Find a 99% confidence interval for₁-₂. (Round your answers to two decimal places.)

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On the Navajo Reservation, a random sample of228permanent dwellings in the Fort Defiance region showed that64were traditional Navajo hogans. In the Indian Wells region, a random sample of137permanent dwellings showed that21were traditional hogans. Letp₁be the population proportion of all traditional hogans in the Fort Defiance region, and letp₂be the population proportion of all traditional hogans in the Indian Wells region.

(a) Find a90%confidence interval forp₁-p₂. (Use 3 decimal places.)

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