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 o of approximately 8°F. A 20-year study (620 July days) gave the entries in the rightmost column of the following table II III IV Observed Region under Normal Curve Expected % from Normal Curve Number of Days in 20 Years х°F μ- 3σ

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

(ii) Use a 1% level of significance to test the claim that the average daily July temperature follows a normal distribution with μ = 75 and σ = 8.

(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?
 
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 o of approximately 8°F. A 20-year study (620 July days) gave the entries in the rightmost column of the following table
II
III
IV
Observed
Region under
Normal Curve
Expected % from
Normal Curve
Number of Days
in 20 Years
х°F
μ- 3σ<x< μ - 2σ
μ- 2σ x< μ σ
и — о <x<и
μ<x< μ + σ
u + o < x < µ + 2o
u + 20 < x < µ + 3o
51 < x < 59
2.35%
19
86
59 < x < 67
13.5%
67 < x < 75
34%
210
75 < x < 83
83 < x < 91
91 < x < 99
34%
208
13.5%
83
2.35%
14
Area Under a Normal Curve
2.35%
13.5%
34%
34%
13.5%
2.35%
и — За
и - 20
H + 20
u + 30
68%
95%
99.7%
Transcribed Image Text: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 o of approximately 8°F. A 20-year study (620 July days) gave the entries in the rightmost column of the following table II III IV Observed Region under Normal Curve Expected % from Normal Curve Number of Days in 20 Years х°F μ- 3σ<x< μ - 2σ μ- 2σ x< μ σ и — о <x<и μ<x< μ + σ u + o < x < µ + 2o u + 20 < x < µ + 3o 51 < x < 59 2.35% 19 86 59 < x < 67 13.5% 67 < x < 75 34% 210 75 < x < 83 83 < x < 91 91 < x < 99 34% 208 13.5% 83 2.35% 14 Area Under a Normal Curve 2.35% 13.5% 34% 34% 13.5% 2.35% и — За и - 20 H + 20 u + 30 68% 95% 99.7%
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