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A manufacturer of light bulbs advertises that on average

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A manufacturer of light bulbs advertises that, on average, its long-life bulb will last more than 5000 hours. To test the claim, a statistician took a random sample of 100 bulbs and measured the amount of time until each bulb burned out.  If we assume that the lifetime of this type of bulb has a standard deviation of 400 hours, can we conclude at the 5% significance level that the claim is true?

Bulbs:
4531
4061
5361
4805
5334
5128
5129
5058
4592
4445
5141
4878
5525
4686
4908
4550
4957
5496
4277
5012
4933
5237
4891
5427
5486
5287
4791
4789
4916
4508
5208
4316
4354
5088
4420
4968
5105
4980
4842
5067
4877
5486
5271
5461
5469
4335
5338
5454
5132
5220
5490
5054
5167
5057
5725
5202
4393
5273
5244
4966
4918
5820
5493
5007
5156
5651
5243
5012
5122
5855
4623
5269
5374
5140
4716
4714
5016
5371
5267
5796
5034
5356
6046
5193
4670
4542
5034
3872
4951
5103
5631
5250
4768
4299
5032
5483
5570
5235
4943
5820

Reference no: EM13609507

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