Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in July in a town in Colorado. The x distribution has a mean ? of approximately 75°F and standard deviation ? of approximately 8°F. A 20-year study (620 July days) gave the entries in the rightmost column of the following table. I II III IV Region under Normal Curve x°F Expected % from Normal Curve Observed Number of Days in 20 Years μ – 3σ ≤ x < μ – 2σ 51 ≤ x < 59 2.35% 15 μ – 2σ ≤ x < μ – σ 59 ≤ x < 67 13.5% 90 μ – σ ≤ x < μ 67 ≤ x < 75 34% 205 μ ≤ x < μ + σ 75 ≤ x < 83 34% 213 μ + σ ≤ x < μ + 2σ 83 ≤ x < 91 13.5% 86 μ + 2σ ≤ x < μ + 3σ 91 ≤ x < 99 2.35% 11 Use a 1% level of significance (i) Remember that ? = 75 and ? = 8. Examine the figure above. Write a brief explanation for columns I, II, and III in the context of this problem. (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?

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 July in a town in Colorado. The x distribution has a mean ? of approximately 75°F and standard deviation ? of approximately 8°F. A 20-year study (620 July days) gave the entries in the rightmost column of the following table.

I	II	III	IV
Region under Normal Curve	x°F	Expected % from Normal Curve	Observed Number of Days in 20 Years
μ – 3σ ≤ x < μ – 2σ	51 ≤ x < 59	2.35%	15
μ – 2σ ≤ x < μ – σ	59 ≤ x < 67	13.5%	90
μ – σ ≤ x < μ	67 ≤ x < 75	34%	205
μ ≤ x < μ + σ	75 ≤ x < 83	34%	213
μ + σ ≤ x < μ + 2σ	83 ≤ x < 91	13.5%	86
μ + 2σ ≤ x < μ + 3σ	91 ≤ x < 99	2.35%	11

Use a 1% level of significance

(i) Remember that ? = 75 and ? = 8. Examine the figure above. Write a brief explanation for columns I, II, and III in the context of this problem.

(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?

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