Independent random samples were selected from populations 1 and 2. The sample sizes , means , and variances are as follows .Population*Sample Size3564Sample Mean12 . 28 . 1Sample Variance*1 . 374. 13( a ) Find a 95% confidence interval for estimating the difference in the population means ( 1 1 – 12 ) . ( Round your answers to two decimal places . )( b ) Based on the confidence interval in part ( a ) , can you conclude that there is a difference in the means for the two populations ? Explain ."Since the value 1 1 – 12 = O is not in the confidence interval , it is likely that there is a difference in the population means ."Since the value 1 1 – 12 = 0 is in the confidence interval , it is likely that there is a difference in the population means ."Since the value #1 – 12 = O is not in the confidence interval , it is not likely that there is a difference in the population means .Since the value 1 1 – 12 = O is in the confidence interval , it is not likely that there is a difference in the population means .You may need to use the appropriate appendix table or technology to answer this question ."Need Help ? [[ Read It\Talk to a Tutor*\$ – 12 points Mend Stat1 4 8 . E. 057 .[ My Notes & Ask Your TeacherFor the proportion of red candies in peanut M&M’S . )( a ) Construct a 95% confidence interval for the difference in the proportions of red candies for the plain and peanut varieties ( P 1 – P 2 ) . ( Round your answers to three decimal places . )to*( b ) Based on the confidence interval in part ( a ) , can you conclude that there is a difference in the proportions of red candies for the plain and peanut varieties ? Explain ."Since the value p 1 – P 2 = O is not in the confidence interval , It is possible that P1 = P 2. We should not conclude that there is a difference in the proportion of red candies in plain and peanut M&M’s .Since the value P1 – P2 = O is not in the confidence interval , it is possible that P 1 = P2 . We should conclude that there is a difference in the proportion of red candies in plain and peanut M&M’S ."Since the value p1 – P2 = 0 is in the confidence interval , it is possible that P1 = P2 . We should conclude that there is a difference in the proportion of red candies in plain and peanut M&M’S .Since the value p 1 – P2 = 0 is in the confidence interval , it is possible that P1 = P2 . We should not conclude that there is a difference in the proportion of red candies in plain and peanut M&M’S ."You may need to use the appropriate appendix table or technology to answer this question ."Need Help ? [Read It]It ][ Talk to a Tutor** – 12 points Mend Stat1 4 8 . E. DGO .[ My Notes . Ask Your Teachermeet quotas , and talking to a manager rather than a salesperson . Suppose that random samples of 400 men and 400 women are taken , and that the men were more likely than the women to say they* alwayIlways or often " bargained ( 30 % compared with 25% ) . ( Use p 1 and p2 for the proportions ofmen and women , respectively , who say they " always or often " negotiate for a better deal . )( a ) Construct a 95% confidence interval for the difference in the proportion of men and women who say they " always or often " negotiate for a better deal . ( Round your answers to three decimal places . )to( b ) Do the data indicate that there is a difference in the proportion of men and women who say they " always or often " negotiate for a better deal ? Explain .“. Since the value P1 – P 2 = O is in the confidence interval , it is possible that P1 – P 2 = O . We should conclude that there is a difference in the proportion of men versus women who say they " always or often " negotiate for a better deal .*Since the value P 1 – P2 = 0 is in the confidence interval , it is possible that P 1 – P 2 = 0 . We should not conclude that there is a difference in the proportion of men versus women who say they " always or often " negotiate for a better deal .Since the value p1 – P 2 = O is not in the confidence interval , it is not possible that P 1 – P 2 = O . We should not conclude that there is a difference in the proportion of men versus women who say they " always or often " negotiate for a better deal .` Since the value p1 – P2 = 0 is not in the confidence interval , it is not possible that P 1 – 2 = 0 . We should conclude that there is a difference in the proportion of men versus women who say they " always or often " negotiate for a better deal .*You may need to use the appropriate appendix table or technology to answer this question ."