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Description: A random sample of statistics students were asked to estimate the total number of hours they spend watching television in an average week. The responses are recorded in the table below. Use this sample data to construct a 90% confidence interval for

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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A random sample of statistics students were asked to estimate the total number of hours they spend watching television in an average week. The responses are recorded in the table below. Use this sample data to construct a 90% confidence interval for the mean number of hours statistics students will spend watching television in one week.

0	3	1	20	9
5	10	1	10	4
14	2	4	4	5

Round the mean, standard deviation and EBM to 4 places, then round answer to 2 places at the end.

Fill in the blank, round to two decimal places:

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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Step 1

Confidence Interval: A confidence interval, in statistics, refers to the probability that a population parameter will fall between the two set values for a certain proportion of times. confidence interval measures the degree of uncertainty or certainty in a sampling method.

Mean: The mean is the sum of observations divided by number of observations. that is,
Mean = $x = \frac{S u m o f t h e o b s e r v a t i o n}{N u m b e r o f o n s e r v a t i o n}$
Notations:
Sample mean = $x$ and
Population mean = μ

Variance: The variance is the expectation of the squared deviation of a random variable from it's a mean. from the variance we can conclude that how far set of numbers is spread out from their average value.

Sample standard deviation formula:

$s = \sqrt{\frac{\sum_{} {(x_{i} - x)}^{2}}{n - 1}}$

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