Consider the following table present the confidence interval lengths as function of n

given standard deviation s = 2.

alpha=0.05 n=25:400

2*qt(1-alpha/2,n-1)*s/sqrt(n)

[1] 1.6511188 1.6156350 1.5823473 1.5510381 1.5215186 1.4936245 1.4672118

[8] 1.4421538 1.4183383 1.3956660 1.3740481 1.3534053 1.3336664 1.3147673 [15]

1.2966500 1.2792621 1.2625558 1.2464877 1.2310183 1.2161112 1.2017330

[22] 1.1878534 1.1744440 1.1614789 1.1489341 1.1367874 1.1250181 1.1136071

[29] 1.1025365 1.0917898 1.0813515 1.0712070 1.0613429 1.0517464 1.0424057

[36] 1.0333096 1.0244476 1.0158098 1.0073870 0.9991703 0.9911515 0.9833227

[43] 0.9756767 0.9682063 0.9609049 0.9537663 0.9467846 0.9399539 0.9332691

[50] 0.9267248 0.9203164 0.9140392 0.9078886 0.9018606 0.8959512 0.8901564

[57] 0.8844726 0.8788964 0.8734243 0.8680532 0.8627800 0.8576018 0.8525157

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1 2

[64] 0.8475190 0.8426092 0.8377838 0.8330403 0.8283765 0.8237902 0.8192793

[71] 0.8148416 0.8104753 0.8061785 0.8019493 0.7977859 0.7936868 0.7896502

[78] 0.7856746 0.7817584 0.7779002 0.7740986 0.7703522 0.7666596 0.7630197

[85] 0.7594311 0.7558927 0.7524033 0.7489618 0.7455671 0.7422182 0.7389139

[92] 0.7356535 0.7324358 0.7292599 0.7261250 0.7230302 0.7199747 0.7169576

[99] 0.7139780 0.7110354 0.7081288 0.7052576 0.7024210 0.6996184 0.6968490 [106]

0.6941123 0.6914076 0.6887343 0.6860917 0.6834793 0.6808966 0.6783429

[113] 0.6758177 0.6733205 0.6708508 0.6684081 0.6659918 0.6636016 0.6612370

[120] 0.6588974 0.6565825 0.6542918 0.6520250 0.6497815 0.6475611 0.6453632

[127] 0.6431876 0.6410338 0.6389015 0.6367904 0.6347001 0.6326302 0.6305804 [134]

0.6285505 0.6265400 0.6245486 0.6225762 0.6206223 0.6186867 0.6167691

[141] 0.6148692 0.6129868 0.6111216 0.6092732 0.6074416 0.6056264 0.6038273

[148] 0.6020442 0.6002768 0.5985249 0.5967882 0.5950665 0.5933597 0.5916675

[155] 0.5899897 0.5883260 0.5866764 0.5850405 0.5834183 0.5818095 0.5802139

[162] 0.5786314 0.5770617 0.5755048 0.5739604 0.5724284 0.5709085 0.5694007

[169] 0.5679048 0.5664206 0.5649480 0.5634869 0.5620370 0.5605982 0.5591705

[176] 0.5577535 0.5563473 0.5549517 0.5535666 0.5521917 0.5508271 0.5494725

[183] 0.5481279 0.5467931 0.5454679 0.5441524 0.5428464 0.5415497 0.5402623

[190] 0.5389840 0.5377147 0.5364543 0.5352028 0.5339600 0.5327258 0.5315002

[197] 0.5302829 0.5290740 0.5278733 0.5266808 0.5254963 0.5243197 0.5231510

[204] 0.5219901 0.5208369 0.5196913 0.5185533 0.5174226 0.5162994 0.5151834

[211] 0.5140746 0.5129730 0.5118784 0.5107908 0.5097100 0.5086362 0.5075690

[218] 0.5065086 0.5054548 0.5044075 0.5033668 0.5023324 0.5013044 0.5002826

[225] 0.4992671 0.4982578 0.4972545 0.4962573 0.4952661 0.4942808 0.4933013

[232] 0.4923276 0.4913597 0.4903975 0.4894409 0.4884899 0.4875443 0.4866043

[239] 0.4856697 0.4847404 0.4838165 0.4828978 0.4819844 0.4810761 0.4801729

[246] 0.4792748 0.4783817 0.4774935 0.4766104 0.4757320 0.4748586 0.4739899

[253] 0.4731260 0.4722667 0.4714122 0.4705623 0.4697169 0.4688761 0.4680398

[260] 0.4672079 0.4663805 0.4655574 0.4647387 0.4639243 0.4631142 0.4623082

[267] 0.4615065 0.4607090 0.4599155 0.4591262 0.4583409 0.4575596 0.4567823

[274] 0.4560089 0.4552395 0.4544739 0.4537122 0.4529543 0.4522002 0.4514498

[281] 0.4507032 0.4499602 0.4492210 0.4484853 0.4477533 0.4470248 0.4462999

[288] 0.4455784 0.4448605 0.4441461 0.4434350 0.4427274 0.4420231 0.4413222

[295] 0.4406246 0.4399304 0.4392393 0.4385516 0.4378670 0.4371857 0.4365075

[302] 0.4358325 0.4351606 0.4344918 0.4338260 0.4331633 0.4325037 0.4318470

13

[309] 0.4311933 0.4305426 0.4298949 0.4292500 0.4286080 0.4279689 0.4273327

[316] 0.4266993 0.4260687 0.4254408 0.4248158 0.4241935 0.4235739 0.4229570

[323] 0.4223429 0.4217313 0.4211225 0.4205162 0.4199126 0.4193116 0.4187131

[330] 0.4181172 0.4175238 0.4169330 0.4163446 0.4157588 0.4151754 0.4145944

[337] 0.4140159 0.4134398 0.4128661 0.4122948 0.4117258 0.4111592 0.4105949

[344] 0.4100329 0.4094733 0.4089159 0.4083608 0.4078080 0.4072574 0.4067090

[351] 0.4061628 0.4056188 0.4050770 0.4045374 0.4039999 0.4034645 0.4029313

[358] 0.4024002 0.4018712 0.4013442 0.4008194 0.4002965 0.3997758 0.3992570

[365] 0.3987403 0.3982255 0.3977128 0.3972020 0.3966932 0.3961863 0.3956814 [372]

0.3951784 0.3946773 0.3941782 0.3936809 0.3931855

For what value of n, the confidence interval at level 95% will have roughly the same

length as the 90% confidence interval for n = 50?