4 Determine the t-value in each of the cases.Click the icon to view the table of areas under the t-distribution.(a) Find the t-value such that the area in the right tail is 0.15 with 8 degrees of freedom.(Round to three decimal places as needed.)(b) Find the t-value such that the area in the right tail is 0.20 with 27 degrees of freedom.(Round to three decimal places as needed.)(c) Find the t-value such that the area left of the t-value is 0.02 with 13 degrees of freedom. [Hint: Use symmetry.](Round to three decimal places as needed.)(d) Find the critical t-value that corresponds to 98% confidence. Assume 16 degrees of freedom.(Round to three decimal places as needed.) -Area inright tailTable VIt-DistributionArea in Right Taildf0.250.200.150.100.050.0250.020.010.0050.00250.0010.00056.314127.32114.0897.4535.59811.3761.9631.3861.2501.1903.07812.70615.89431.8216.9654.54163.6579.9255.8411.000318.309636.6192.9202.3532.13231.5990.81630.76540.74121.0610.9780.9410.9201.8861.6381.5334.3033.1822.7764.8493.4822.99922.32710.21512.9247.1735.8933.7474.6048.6100.7271.1561.4762.0152.5712.7573.3654.0324.7736.8691.1342.6122.5172.4492.3982.3595.9595.4080.7180.9060.8961.4401.4151.3971.3831.3721.9431.8951.8602.4473.1432.9983.7073.4993.3553.2504.3175.2082.3652.3062.2622.2284.7854.5014.29770.7111.1194.0290.7060.7030.8890.8830.8791.1081.1002.8962.8212.7643.8333.6903.5815.0414.7811.833100.7001.0931.8123.1694.1444.5871.7964.0253.930110.6970.6950.6940.6920.8760.8730.8700.8681.0881.0831.0791.3631.3561.3501.3451.3412.2012.3282.3032.2822.2642.2492.7182.6812.6503.1063.0553.0123.4974.4371.7821.7711.7613.4283.3722.17912134.3183.8523.7873.7332.1604.2212.9772.9472.14514151.0762.6243.3264.1400.6910.8661.0741.7532.1312.6023.2864.073160.6900.8651.0711.3371.3331.7462.1202.2352.5832.5672.9213.2523.2223.6863.6464.0153.965170.6890.8631.0691.7402.1102.2242.898

Given : To find : t valuesolution : a) Degree of freedom = 8 cumulative probability,p= 0.15 Now p(T > t)= 0.15 p(T > 1.108 )= 0.15 ......using student t distribution table ) i.e t= 1.108b) Degree of freedom = 27 cumulative probability,p= 0.2 Now p(T > t)= 0.2 p(T > 0.855 )= 0.2 ......using student t distribution table ) i.e t= 0.855 c) Degree of freedom = 13 cumulative probability,p= 0.02 Now p(T <t)= 0.02 p(T< -2.282 )= 0.02 (......using student t distribution table ) i.e t= -2.282d) critical value : critical value with df = 16 and α = 1-98/100 = 0.02 is t = 2.583

Math

Statistics

Click the icon to view the table of areas under the t-distribution. (a) Find the t-value such that the area in the right tail is 0.15 with 8 degrees of freedom. (Round to three decimal places as needed.) (b) Find the t-value such that the area in the right tail is 0.20 with 27 degrees of freedom. (Round to three decimal places as needed.) (c) Find the t-value such that the area left of the t-value is 0.02 with 13 degrees of freedom. [Hint: Use symme (Round to three decimal places as needed.) (d) Find the critical t-value that corresponds to 98% confidence. Assume 16 degrees of freedom. (Round to three decimal places as needed.)