A random sample of 18 venture-capital investments in a certain business sector yielded the accompanying data, in millions of dollars. Assuming that the population standard deviation is $1.82 million, a 95% confidence interval for the mean amount, μ, of all venture-capital investments in this business sector is from $5.87 million to $7.55 million. Conditions for computing the confidence interval are satisfied. Complete parts (a) through (d) below. (Note: The sum of the data is $120.73 million and the mean is $6.71 million.) a. Find a 90% confidence interval for μ. The 90% confidence interval is from $______million to $_million. (Round to two decimal places as needed.) b. Why is the confidence interval you found in part (a) shorter than the 95% confidence interval? The______used in computing the confidence interval found in part (a) is_the corresponding value for the 95% confidence interval. c. Draw a graph to display both confidence intervals. d. Which confidence interval yields a more accurate estimate of μ? Explain your answer. The 90% confidence interval yields a more accurate estimate of μ, since____________________.

Name: A random sample of 18 venture-capital investments in a certain busine
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Description: A random sample of 18 venture-capital investments in a certain business sector yielded the accompanying data, in millions of dollars. Assuming that the population standard deviation is $1.82 million, a 95% confidence interval for the mean amount

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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A random sample of 18 venture-capital investments in a certain business sector yielded the accompanying data, in millions of dollars. Assuming that the population standard deviation is $1.82 million, a 95% confidence interval for the mean amount,

μ, of all venture-capital investments in this business sector is from $5.87 million to $7.55 million. Conditions for computing the confidence interval are satisfied. Complete parts (a) through (d) below. (Note: The sum of the data is $120.73 million and the mean is $6.71 million.)

a. Find a 90% confidence interval for μ.

The 90% confidence interval is from $__________million to $_______million.

(Round to two decimal places as needed.)

b. Why is the confidence interval you found in part (a) shorter
than the 95% confidence interval?

The____________used in computing the confidence interval found in part (a) is_________the corresponding value for the 95% confidence interval.

c. Draw a graph to display both confidence intervals.

d. Which confidence interval yields a more accurate estimate of μ? Explain your answer.

The 90% confidence interval yields a more accurate estimate of μ, since________________________.

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 + ...

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