Instruction 10-3
a Real Estate Company Is Interested in Testing $\quad \bar { X } _ { G } = 35$

question 86

Multiple Choice

Instruction 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: $\quad \bar { X } _ { G } = 35$ months, $S _ { G } { } ^ { 2 } = 900$
Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$
-Referring to Instruction 10-3,suppose $\alpha$ = 0.10.Which of the following represents the correct conclusion?

• A) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
• B) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
• C) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.
• D) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.

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Definitions:

Continuous Random Variable

A variable that can take an infinite number of values within a given range, with each possible value being associated with a probability.

Random Variable

A variable whose numerical values result from a random phenomenon or statistical experiment.

Constant

In mathematics and statistics, a fixed value that does not change within the scope of a given problem.

Interval

A range between two numbers or points, often used to specify a period of time or a statistical range.