You may need to use the appropriate appendix table or technology to answer this question.Americans spend nearly $7 billion on Halloween costumes and decorations.† Sample data showing the amount, in dollars, 16 adults spent on a Halloween costume are as follows.33644531693652264413983263221612(a)What is the estimate of the population mean amount (in dollars) adults spend on a Halloween costume?$ (b)What is the sample standard deviation (in dollars)? (Round your answer to the nearest cent.)$ (c)Provide a 95% confidence interval estimate of the population standard deviation (in dollars) for the amount adults spend on a Halloween costume. (Round your answers to the nearest cent.)$ to $ **Educational Content: Analyzing Halloween Costume Spending****Context:**Americans spend approximately $7 billion on Halloween costumes and decorations. A sample data set provides insight into the spending habits of 16 adults regarding their Halloween costumes.**Sample Data:**The table below presents the amount spent (in dollars) by each of the 16 adults:\[\begin{array}{cccc}33 & 64 & 45 & 31 \\69 & 36 & 52 & 26 \\44 & 13 & 98 & 32 \\63 & 22 & 16 & 12 \\\end{array}\]**Analysis Tasks:**(a) **Estimate of Population Mean:**Determine the average amount (in dollars) adults spend on a Halloween costume. This requires calculating the mean of the given sample data.(b) **Sample Standard Deviation:**Compute the sample standard deviation (in dollars) and round the answer to the nearest cent. This measures the variation or dispersion of the spending data from the mean.(c) **95% Confidence Interval:**Provide a 95% confidence interval estimate for the population standard deviation (in dollars) regarding adult Halloween costume spending. This interval gives a range within which we expect the population standard deviation to fall, with 95% confidence. Round the answers to the nearest cent. **Graphical Representation:**This section would typically include graphs or diagrams if applicable. In this case, interpreting the data through summary statistics (mean and standard deviation) and providing confidence intervals helps visualize the variability and central tendency of the sample.**Conclusion:**By understanding the sample's mean, standard deviation, and confidence intervals, we gain insights into overall spending trends, variability in spending, and the likely range of average costs across a broader population.

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Description: You may need to use the appropriate appendix table or technology to answer this question.Americans spend nearly $7 billion on Halloween costumes and decorations.† Sample data showing the amount, in dollars, 16 adults spent on a Halloween costume are

a) The sample mean is the estimate of the population mean amount. Thus, the required sample mean can…

Answered: You may need to use the appropriate…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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You may need to use the appropriate appendix table or technology to answer this question.

Americans spend nearly $7 billion on Halloween costumes and decorations.† Sample data showing the amount, in dollars, 16 adults spent on a Halloween costume are as follows.

33	64	45	31
69	36	52	26
44	13	98	32
63	22	16	12

(a)

What is the estimate of the population mean amount (in dollars) adults spend on a Halloween costume?

(b)

What is the sample standard deviation (in dollars)? (Round your answer to the nearest cent.)

(c)

Provide a 95% confidence interval estimate of the population standard deviation (in dollars) for the amount adults spend on a Halloween costume. (Round your answers to the nearest cent.)

$ to $

**Educational Content: Analyzing Halloween Costume Spending**

**Context:**
Americans spend approximately $7 billion on Halloween costumes and decorations. A sample data set provides insight into the spending habits of 16 adults regarding their Halloween costumes.

**Sample Data:**
The table below presents the amount spent (in dollars) by each of the 16 adults:

\[
\begin{array}{cccc}
33 & 64 & 45 & 31 \\
69 & 36 & 52 & 26 \\
44 & 13 & 98 & 32 \\
63 & 22 & 16 & 12 \\
\end{array}
\]

**Analysis Tasks:**

(a) **Estimate of Population Mean:**
Determine the average amount (in dollars) adults spend on a Halloween costume. This requires calculating the mean of the given sample data.

(b) **Sample Standard Deviation:**
Compute the sample standard deviation (in dollars) and round the answer to the nearest cent. This measures the variation or dispersion of the spending data from the mean.

(c) **95% Confidence Interval:**
Provide a 95% confidence interval estimate for the population standard deviation (in dollars) regarding adult Halloween costume spending. This interval gives a range within which we expect the population standard deviation to fall, with 95% confidence. Round the answers to the nearest cent.

**Graphical Representation:**
This section would typically include graphs or diagrams if applicable. In this case, interpreting the data through summary statistics (mean and standard deviation) and providing confidence intervals helps visualize the variability and central tendency of the sample.

**Conclusion:**
By understanding the sample's mean, standard deviation, and confidence intervals, we gain insights into overall spending trends, variability in spending, and the likely range of average costs across a broader population.

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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