Since P-value is greater than, less than or equal to, the signifance level, reject or fail to reject the null hypothesis. There is or is not sufficient to support the claim that presidents tends to be taller than their opponents. Since the confidence interval contains zero, only positive numbers, or only negative numbers | fail to reject or reject the null hypothesis. 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 | 180 | 186 | 176 | 168 | 179 | 171 ||---|---|---|---|---|---|---|| Height (cm) of Main Opponent | 168 | 175 | 164 | 178 | 191 | 179 |---a. Use the sample data with a 0.01 significance level to test the claim that for the population of heights for presidents and their main opponents, the differences have a mean greater than 0 cm.In this example, \(\mu_d\) is the mean value of the differences \(d\) for the population of all pairs of data, where each individual difference \(d\) is defined as the president's height minus their main opponent's height. What are the null and alternative hypotheses for the hypothesis test?- \(H_0: \mu_d \leq 0\) cm- \(H_1: \mu_d > 0\) cmIdentify the test statistic.- \(t =\) [Round to two decimal places as needed.]Identify the P-value.- P-value = [Round to three decimal places as needed.]What is the conclusion based on the hypothesis test?Since the P-value is [ ] the significance level, [ ] sufficient evidence to support the claim that presidents tend to be taller than their opponents.b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)?- The confidence interval is [ ] cm < \(\mu_d\) < [ ] cm. (Round to one decimal place as needed.)What feature of the confidence interval leads to the same conclusion reached in part (a)?Since the confidence interval contains [ ], [ ] the null hypothesis.

Solution: Let x = President Height and y=Main Opponent height x y d=x-y (d-d)2 180 168 12 34.02778 186 175 11 23.36111 176 164 12 34.02778 188 178 10 14.69444 190 191 -1 51.36111 172 179 -7 173.3611 n=6d =∑dn=376=6.1667 Difference of sample mean sd=∑(d-d)2n-1sd=330.833335sd=8.1343 Differnece of sample standard deviation The null and alternative hypothesis is Ho:μd=0 VS Ha:μd>0 Test statistic t=dsd/nt=6.16678.1343/6t=6.16673.320814=1.856984t=1.86 Test statistic t= 1.86 To find p value p value = P(t>1.86) p value =0.061 From Excel Since P-value is greater than the significance level fail to reject the null hypothesis. There is not sufficient to support the claim that presidents tends to be taller than their opponents. b) The 99% confidence interval for the difference of means is d±tα/2,n-1×sdnAt α=0.01tα/2,n-1=t0.005,5=4.032 From t table 6.1667±4.032×8.13436(6.1667±4.032×3.320814)(6.1667±13.389522)(-7.2228, 19.5562)(-7.2, 19.6) The confidence interval is -7.2 cm<μd<19.6 cm Since the confidence interval contains zero, fail to reject the null hypothesis.