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.

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