The following problem is based on information from the National Oceanic and Atmospheric Administration (NOAA) Environmental Data Service. Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in July in the town of Kit Carson, Colorado. The x distribution has a mean μ of approximately 75oF and standard deviation s of approximately 8oF. A 20-year study (620 July days) gave the entries in the rightmost column of the following table:

(i) Remember that μ = 75 and σ = 8. Examine Figure 7-3 in Chapter 7. 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.
Please provide the following information.
(a) What is the level of significance? State the null and alternate hypotheses.
(b) Find the value of the chi-square statistic for the sample. Are all the expected frequencies greater than 5? What sampling distribution will you use? What are the degrees of freedom?
(c) Find or estimate the P-value of the sample test statistic.
(d) Based on your answers in parts (a)€“(c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?
(e) Your conclusion in the context of the application.

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Observed Region under Normal Curve Expected % from Normal Curve Number of Days in 20 Years 2.35% 13.5% 3490 34% 13.5% 2.35% 16 78 212 221 81 12 59 sx 67 67 sx < 75