a, we fail to reject the null hypothesis.O Since the P-value > a, we reject the null hypothesis.O Since the P-value s a, we reject the null hypothesis.O Since the P-value s a, we fail to reject the...


Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in January for a town in Hawaii. The x variable has<br>mean u of approximately 68°F and standard deviation o of approximately 4°F. A 20-year study (620 January days) gave the entries in the rightmost column of the following table.<br>II<br>III<br>IIII<br>Region under<br>Normal Curve<br>Expected % from<br>Normal Curve<br>Observed Number of<br>x°F<br>Days in 20 Years<br>u - 30 sx <u - 20<br>u - 20 sx <u - o<br>u - osx < u<br>u<x < H + o<br>u + osx <u + 20<br>u + 20 s x <u + 30<br>56 sx < 6o<br>2.35%<br>18<br>60 s x < 64<br>64 s x < 68<br>68 < x < 72<br>72 sx < 76<br>76 Sx < 80<br>13.5%<br>88<br>34%<br>34%<br>216<br>202<br>13.5%<br>87<br>2.35%<br>9<br>(i) Remember that u = 68 and o = 4. Examine the Normal Distribution Curve. Write a brief explanation for columns I, II, and III in the context of this problem.<br>(ii) Use a 1% level of significance to test the claim that the average daily January temperature follows a normal distribution with u = 68 and o = 4.<br>(a) What is the level of significance?<br>State the null and alternate hypotheses.<br>O Ho: The distributions are the same.<br>H,: The distributions are the same.<br>O Ho: The distributions are the same.<br>H,: The distributions are different.<br>O Ho: The distributions are different.<br>H,: The distributions are the same.<br>O Ho: The distributions are different.<br>H,: The distributions are different.<br>(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.)<br>Are all the expected frequencies greater than 5?<br>O Yes<br>O No<br>What sampling distribution will you use?<br>O uniform<br>O normal<br>O Student's t<br>O binomial<br>O chi-square<br>What are the degrees of freedom?<br>(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)<br>(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?<br>O Since the P-value > a, we fail to reject the null hypothesis.<br>O Since the P-value > a, we reject the null hypothesis.<br>O Since the P-value s a, we reject the null hypothesis.<br>O Since the P-value s a, we fail to reject the null hypothesis.<br>(e) Interpret your conclusion in the context of the application.<br>O At the 1% level of significance, the evidence is sufficient to conclude that the average daily January temperature does not follow a normal distribution.<br>O At the 1% level of significance, the evidence is insufficient to conclude that the average daily January temperature does not follow a normal distribution.<br>

Extracted text: Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in January for a town in Hawaii. The x variable has mean u of approximately 68°F and standard deviation o of approximately 4°F. A 20-year study (620 January days) gave the entries in the rightmost column of the following table. II III IIII Region under Normal Curve Expected % from Normal Curve Observed Number of x°F Days in 20 Years u - 30 sx

a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Since the P-value s a, we reject the null hypothesis. O Since the P-value s a, we fail to reject the null hypothesis. (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 January temperature does not follow a normal distribution. O At the 1% level of significance, the evidence is insufficient to conclude that the average daily January temperature does not follow a normal distribution.
Jun 11, 2022
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