Assuming that the number of birds is normally distributed, approximate a 90% confidence intervalfor the actual mean. 4.In a research study a group of 10 students were asked to count the number of birds theysaw in a park over a one hour period. Their counts were:102, 95, 101, 94, 93, 106, 92, 87, 104, 105(a) Write down formulas for unbiased estimators for the expected value (actual mean) and variancefrom a sample of size 10.(b) Write down a formula for a biased estimator for the standard deviation from a sample of size 10.(c) Using these formulas or otherwise, calculate the sample mean and sample standard deviation ofthis data.

Let the number of birds seen by students.Data: Xi1029510194931069287104105To determine the CI for…

Answered: In a research study a group of 10…

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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Assuming that the number of birds is normally distributed, approximate a 90% confidence interval
for the actual mean.

4.
In a research study a group of 10 students were asked to count the number of birds they
saw in a park over a one hour period. Their counts were:
102, 95, 101, 94, 93, 106, 92, 87, 104, 105
(a) Write down formulas for unbiased estimators for the expected value (actual mean) and variance
from a sample of size 10.
(b) Write down a formula for a biased estimator for the standard deviation from a sample of size 10.
(c) Using these formulas or otherwise, calculate the sample mean and sample standard deviation of
this data.

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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