Question

A popular theory is that presidential candidates have an advantage if they are taller than their main opponents 'Listed are heights (in centimeters) of randomly selected presidents along with the heights of their main opponents Complete parts (a) and (b) below Height (cm) of President 191 182 184 175 188 167 D Height (cm) of Main Opponent 182 177 181 181 181 181 UPPER LILLE PIVOU LIPS Ho to cm H, Hd cm (Type integers or decimals. Do not round) vo vo 0,0 More

help please

Answer 1

Solution: The following table is obtained: Sample 1 Sample 2 Difference = Sample 1 - Sample 2 191 182 9 182 177 ол 184 181 3 175 181 -6 188 181 7 167 181 -14 Average 181.167 180.5 0.667 St. Dev. 8.841 1.761 8.869 n 6 6 From the sample data, it is found that the corresponding sample means are: X1 = 181.167 X2 = 180.5 Also, the provided sample standard deviations are: 81 = 8.841 S2 = 1.761 and the sample size is n = 6. For the score differences we have D = 0.667 SD = 8.869 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: up = 0 Ha: pp > 0 This corresponds to a right-tailed test, for which a t-test for two paired samples be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the degrees of freedom are df = 5. Hence, it is found that the critical value for this right-tailed test is to = 2.015, for a = 0.05 and df = 5. The rejection region for this right-tailed test is R=t:t > 2.015. (3) Test Statistics The t-statistic is computed as shown in the following formula: D sp/vn 0.667 8.869/6 0.184 (4) Decision about the null hypothesis Since it is observed that t = 0.184 < t = 2.015, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.4306, and since p= 0.4306 > 0.05, it is concluded that the null hypothesis is not rejected.

(5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean ui is greater than um, at the 0.05 significance level. Confidence Interval The 95% confidence interval is –8.641 < up < 9.975. Graphically. p-value = Test 0.43057875824909 0.40 0.35 0.30 1 0.25 0.20 0.15 1 0.10 0.05 0.00 -4.0 -3.5 -3.0 -25 -20 -1.5 -1.0 -0.5 0.0 0.5 10 15 2. 2.5 3.0 3.5 4.0