Answered: Virginia 30083, 32159, 31009, 34384,…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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Question

In a current study, a random sample of 10 teachers from Texas and an independent random sample of 10 teachers from Virginia have been asked to report their annual income. The data obtained are as follows. (See attachment for data table and full question).

The population standard deviations for the annual incomes of teachers in Texas and in Virginia are estimated as $6100 and $6600, respectively. It is also known that both populations are approximately normally distributed. Construct a 95% confidence interval for the difference −μ1μ2 between the mean annual income of teachers from Texas (μ1) and the mean annual income of teachers from Virginia (μ2). Then find the lower limit and upper limit of the 95% confidence interval.

Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places.

a.) The Lower Limit is:

b.) The Upper Limit is:

?
In a current study, a random sample of 10 teachers from Texas and an independent random sample of 10 teachers from
Virginia have been asked to report their annual income. The data obtained are as follows.
Annual income in dollars
Texas 39907, 23242, 36328, 34628, 42540, 44708, 34717, 45291, 27064, 31139
Virginia 30083, 32159, 31009, 34384, 38196, 35798, 43330, 26261, 44537, 35679
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The population standard deviations for the annual incomes of teachers in Texas and in Virginia are estimated as $6100
and $6600, respectively. It is also known that both populations are approximately normally distributed. Construct a 95%
confidence interval for the difference μ₁-₂ between the mean annual income of teachers from Texas (μ₁) and the mean
annual income of teachers from Virginia (μ₂). Then find the lower limit and upper limit of the 95% confidence interval.
Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal
places. (If necessary, consult a list of formulas.)
Lower limit:
Upper limit:
X
Ś
0

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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