Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in January for a town in Hawaii. The x variable has a mean μ of approximately 68°F and standard deviation σ of approximately 4°F. A 20-year study (620 January days) gave the entries in the rightmost column of the following table. I II III IIII Region under Normal Curve x°F Expected % from Normal Curve Observed Number of Days in 20 Years μ – 3σ ≤ x < μ – 2σ 56 ≤ x < 60 2.35% 19 μ – 2σ ≤ x < μ – σ 60 ≤ x < 64 13.5% 78 μ – σ ≤ x < μ 64 ≤ x < 68 34% 202 μ ≤ x < μ + σ 68 ≤ x < 72 34% 220 μ + σ ≤ x < μ + 2σ 72 ≤ x < 76 13.5% 87 μ + 2σ ≤ x < μ + 3σ 76 ≤ x < 80 2.35% 14 (ii) Use a 1% level of significance to test the claim that the average daily January temperature follows a normal distribution with μ = 68 and σ = 4. (a) What is the level of significance? (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.) What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

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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Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in January for a town in Hawaii. The x variable has a mean μ of approximately 68°F and standard deviation σ of approximately 4°F. A 20-year study (620 January days) gave the entries in the rightmost column of the following table.

I	II	III	IIII
Region under Normal Curve	x°F	Expected % from Normal Curve	Observed Number of Days in 20 Years
μ – 3σ ≤ x < μ – 2σ	56 ≤ x < 60	2.35%	19
μ – 2σ ≤ x < μ – σ	60 ≤ x < 64	13.5%	78
μ – σ ≤ x < μ	64 ≤ x < 68	34%	202
μ ≤ x < μ + σ	68 ≤ x < 72	34%	220
μ + σ ≤ x < μ + 2σ	72 ≤ x < 76	13.5%	87
μ + 2σ ≤ x < μ + 3σ	76 ≤ x < 80	2.35%	14

(ii) Use a 1% level of significance to test the claim that the average daily January temperature follows a normal distribution with μ = 68 and σ = 4.

(a) What is the level of significance?

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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