High School

A random sample of 22 adult male wolves from the Canadian Northwest Territories gave an average weight [tex] \bar{x}_1 = 97.8 [/tex] pounds with an estimated sample standard deviation [tex] s_1 = 6.1 [/tex] pounds. Another sample of 23 adult male wolves from Alaska gave an average weight [tex] \bar{x}_2 = 90.6 [/tex] pounds with an estimated sample standard deviation [tex] s_2 = 7.4 [/tex] pounds.

Let [tex] \mu_1 [/tex] represent the population mean weight of adult male wolves from the Northwest Territories, and let [tex] \mu_2 [/tex] represent the population mean weight of adult male wolves from Alaska. Find a 95% confidence interval for [tex] \mu_1 - \mu_2 [/tex]. (Use 1 decimal place.)

- Lower limit: _______
- Upper limit: _______

Answer :

Final answer:

To find a 95% confidence interval for μ1 - μ2, use the formula: CI = (x1 - x2) ± Z * √((s1)²/n1 + (s2)²/n2). Plug in the given values to calculate the confidence interval.

Explanation:

To find a 95% confidence interval for μ1 - μ2, we can use the formula:

CI = (x1 - x2) ± Z * √((s1)²/n1 + (s2)²/n2)

Using the given information:

  • x1 = 97.8
  • s1 = 6.1
  • n1 = 22
  • x2 = 90.6
  • s2 = 7.4
  • n2 = 23
  • Z for a 95% confidence level is approximately 1.96

Plugging in these values, we get:

CI = (97.8 - 90.6) ± 1.96 * √((6.1)²/22 + (7.4)²/23)

Simplifying the expression gives us the 95% confidence interval for μ1 - μ2.

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