Answer Happy

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 u 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 Region under Normal Curve μ - 3σ ζχ <μ - 2σ u - 20 SX<-o μ - σεχ <μ u<x<u+o μ + σεχ <μ + 2σ μ + 2σχ<μ + 3σ X°F 51 < x < 59 59 < X < 67 67 SX< 75 75 < X < 83 83 <x< 91 91 sx < 99 Expected % from Normal Curve 2.35% 13.5% 34% 34% 13.5% 2.35% IV Observed Number of Days in 20 Years 13 83 220 214 76 14 Area Under a Normal Curve 2.35% 13.5% 349 34% 13.5% 2.35% u-30 M-20 -0 uto u + 20 M + 30 68% 95% 99.7% (i) Remember that u = 75 and 0 = 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 j = 75 and 0 = 8. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: The distributions are the same. H: The distributions are the same. O Ho: The distributions are different. H: The distributions are different. O Ho: The distributions are the same. Hj: The distributions are different. O Ho: The distributions are different. Hz: The distributions are the same. (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.) Are all the expected frequencies greater than 5? O Yes O No What sampling distribution will you use? O Student's t O chi-square O binomial O uniform O normal What are the degrees of freedom?

(c) Estimate the P-value of the sample test statistic. OP-value > 0.100 O 0.050 < P-value < 0.100 O 0.025 < P-value < 0.050 O 0.010 < P-value < 0.025 O 0.005 < P-value < 0.010 O p-value < 0.005 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories? O Since the P-value > a, we fail to reject the null hypothesis. Since the P-value > a, we reject the null hypothesis. Since the P-value sa, we reject the null hypothesis. Since the P-value sa, we fail to reject the null hypothesis. оо (e) Interpret your conclusion in the context of the application. O At the 1% level of significance, the evidence is sufficient to conclude that the average daily July temperature does not follow a normal distribution. O At the 1% level of significance, the evidence is insufficient to conclude that the average daily July temperature does not follow a normal distribution.