Question

It is known from previous study that, a product lifetime follow normal distribution and the standard deviation of its is 1 year. Now, an engineer is told that the mean lifetime of its should be 3 years. To verify this, he randomly selects 25 products for testing. He found that average lifetime of the samples is 3.412 years.

Please perform a hypothesis test on the average lifetime of SSD with a p-value threshold of 0.05.

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And I also want to know, for this question, should I use 2 tail test? When should I use 2 tail test? Thank you!

Answer 1

Answeti- life time Pro du CE chistnibution Fo।। ০) deviation =1yet 6 = standaed = 3yeat Mean lifetime ירכןeed tc(C- random Sampie =25 n= N umber OF life time 3.412 average yeat %3D Testi- Hypothe sis:- Nuil =5पा S U= 34eats Mean 1ifetime Hypothe Sis A Het hoative ur 34eats statishcS Test 3 3.412 3-412-3 %3D + 2.06 %3D 12|Y20:05, iF Ho Deasion reje ct Hete = J.64 121 770.08 Here

Thus reject Thus, Pvalue lifetime thart average conclude can be 3412 yeas net may tailed also used (Here d=0.05) d1z 1. 96 1.96 tailed two sill used if both the test is Mean signi ficantly greatee than and if the th an X. mean signifcantHiy The mean js if the Frem Cen Sidered different signi ficantiy bettem top 2.5). in test is the sta bishcs 2.5). porebability distribution , resulting in a of its P- valuO ie ss than