Question

Question 13 20 pts Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Various temperature measurements are recorded at different times during the summer in Holtville on n-60 days. The mean of 8 = 100°F is obtained, with 0 - 10°F. Using the 0.05 significance level, test the claim that the mean temperature is over 995 Hop-100; Hy w 100. Test statistic: 2-0.77. P-value: 0.7794. Because the P-value is greater than the significance level of 0.05, awe reject the null hypothesis. There is sufficient evidence to support the claim that the mean temperature is over 99°F. O Ho: -99: H: > 99. Test statistic: Z-0.77.P-value: 0.2206. Because the P-value is greater than the significance level of 0.05, owe fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the mean temperature is over 99" Question 14 20 pts Find the value of the linear correlation coefficient r. Round your answer to 3 decimal places if necessary. (1.6).(3,4),(5,2) Question 15 20 pts Use the given data to find the equation of the regression line. Round the final values to three places, if necessary. (1.2).(3,4), (5,6) O9--2.79 +0.950x O9--2.79 +0.897%

Answer 1

Question 13 Given that Size of the sample, n = 60 Sample mean, loo Standard deviation, r = 10 hevel of significance = 0.05 Here the claim is that the mean temperature is over 99°F . That is the mean temperature is greater than 99°F. → The null bypothesis, Houle = 99 and the alternative hypothesis, Ha: H>99 Here the sample size is large, so we will you use z test. Thus the test statistic Z = X-Ho ; where Ho-99 100-99 1960 0.77 → Test Statistic ,Z = 0.71 P value P(Z > test statistic ) - P(Z >0.77)

The test is a Right tailed test, since the rejection region is on the right. P value = P(Z >0.77), esiog standard normal table we get P(Z >0.77)- 0.2206 P value If P value is less than or equal to Then reject the pull bypothesis. If p value is greater than ac, we fail to reject he pull bypothesis. 0.2206 Here P value = 0.2206 and x = 0.05 P value is greater than a We fail to reject the null bypothesis → There is not sufficient evidence to support the claim that the mean temperature is Over 99°F . Thus the answer is: Ho! H=99, Hy: H>99. The test statistic :Z=0.77 Pvalue = 0.2206. Because the value is greater than the level of significance 0.05. Owe fail to reject the null bypothesis. There is not Sufficient evidence to Support the claim that the mean tempevature is ovey 99°F.

Question 14 We have to find the correlation coefficient for (1,6), (3, 4), (52) We can write the above points as 1 2 X Y ху 36 3 4. 12 a 5 2 25 4 ΣΧ = 1+3+5 = 9 y = 6+4+2 = 12 OXY = 6+12+ O = 28 I x2 = 1+9+ 25 = 35 I y 36+16+4 = 56 Here D = 3 r= Formula for correlation coefficient r: DEXY-(IX) (EY) [3x?([x]][n3y2– (IY)2] (3x28) - (4x12) (3*35-92) (3x56 - 122) 84 - 108 24 X24 - 24 24

r= -24 = 24 24 -- -1 Thus the correlation coefficient = -1 Thus the answer is r= 1