SLICE NAMEConfidence Intervals and Hypothesis TestingTOPIC NAMEConfidence interval for the population mean: Use of the t distribution Suppose that a random sample of 16 recently sold houses in a certaincity has a mean sales price of $280,000, with a standard deviation of $11,000.Under the assumption that house prices are normally distributed, find a90% confidence interval for the mean sales price of all houses in this city.Give the lower limit and upper limit of the 90% confidence interval.Carry your intermediate computations to at least three decimal places.Round your answers to the nearest whole number. (If necessary, consulta list of formulas.)Lower limit: SUpper limit: $X?BH1FAa

Answered: Suppose that a random sample of 16…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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SLICE NAME Confidence Intervals and Hypothesis Testing TOPIC NAME Confidence interval for the population mean: Use of the t distribution

Suppose that a random sample of 16 recently sold houses in a certain
city has a mean sales price of $280,000, with a standard deviation of $11,000.
Under the assumption that house prices are normally distributed, find a
90% confidence interval for the mean sales price of all houses in this city.
Give the lower limit and upper limit of the 90% confidence interval.
Carry your intermediate computations to at least three decimal places.
Round your answers to the nearest whole number. (If necessary, consult
a list of formulas.)
Lower limit: S
Upper limit: $
X
?
B
H
1
F
Aa

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

We have given that

Sample size (n) = 16
Sample mean (x̅) = 280000
Standard deviations (s) = 11000
Confidence level (c) = 90% = 0.90
Significance level (α) = 1- 0.90 = 0.10