Answered: A scientist estimates that the mean…

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 scientist estimates that the mean nitrogen dioxide level in a city is greater than 34 parts per billion. To test this estimate, you determine the nitrogen dioxide levels for 31 randomly selected days. The results (in parts per billion) are listed to the right. Assume that the population standard deviation is 8. At α=0.03, can you support the scientist's estimate? Complete parts (a) through (e).

14
24
43
32
28
43
40
32
18
36
30
17
17
19
36
43
39
26
20
19
44
23
44
39
30
28
41
33
15
42
22

At α=0.03, can you support the scientist's estimate? Complete parts (a) through (e).

(b) Find the critical value and identify the rejection region.

z0=

(Round to two decimal places as needed.)

Rejection region:

(d) Decide whether to reject or fail to reject the null hypothesis.

At the 3% significance level, there is __________ evidence to

________ the scientist's claim that the mean nitrogen dioxide level in the city is greater than 34 parts per billion.

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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