Construct the Indicated Confidence Interval for the Difference Between the Two

question 48

Multiple Choice

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Independent samples from two different populations yield the following data. $\bar { x } _ { 1 } = 958 , \bar { x } _ { 2 } = 157 , s _ { 1 } = 77 , s _ { 2 } = 88$ . The sample size is 478 for both samples. Find the $85 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ .

• A) \(781 < \mu _ { 1 } - \mu _ { 2 } < 821\)
• B) \(800 < \mu _ { 1 } - \mu _ { 2 } < 802\)
• C) \(794 < \mu _ { 1 } - \mu _ { 2 } < 808\)
• D) \(791 < \mu _ { 1 } - \mu _ { 2 } < 811\)

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Definitions:

T-Distribution

A probability distribution that is used to estimate population parameters when the sample size is small and the population standard deviation is unknown.

Standard Normal Distribution

A normal distribution with a mean of 0 and a standard deviation of 1, used as a basis for comparing other normal distributions.

Finite Population Correction Factor

A statistical adjustment made to the standard error of a sample mean or proportion when sampling without replacement from a finite population.

Sample Size

The number of observations or data points collected from a subset of a larger population in a statistical study.