Question

Preliminary data analyses indicate that it is reasonable to use at test to carry out the specified hypothesis test. Perform the t-test using the critical value approach. A light bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A random sample of 15 of its light bulbs resulted in the following lives in hours. 995 590 510 539 739 917 571 555 916 728 664 093 708 87349 At the 10% significance level do the data provide evidence that the mean life for the company's light bulbs differs from the advertised meant For the toolbar, press ALTF10 POR ALT FN-10 (Mac) TTTT Paragraph All 312001 E.E.T.A. XDOQETT .-- OSO - 16- Phi Words QUESTION 10 Preliminary data analyses indicate this reasonable to use any other pecified the perform the in the preach cancello 0.05 at the theme for winA TTTTA 1 WEB T2 X009 TT 2 OS OSS BIS

Answer 1

1)

Ho :   µ =   900  
Ha :   µ ╪   900   (Two tail test)
          
Level of Significance ,    α =    0.100  
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   153.7142  
Sample Size ,   n =    15  
Sample Mean,    x̅ = ΣX/n =    720.7333  
          
degree of freedom=   DF=n-1=   14  
          
Standard Error , SE = s/√n =   153.7142/√15=   39.6888  
t-test statistic= (x̅ - µ )/SE =    (720.7333-900)/39.6888=   -4.517  
          
critical t value, t* =    ±   1.7613   [Excel formula =t.inv(α/no. of tails,df) ]
          
Decision:  |test stat | > |critical value|, Reject null hypothesis       
conclusion : there is enough evidence to ssy that mean is different than 900

.................

Ho :   µ =   32.6  
Ha :   µ ╪   32.6   (Two tail test)
          
Level of Significance ,    α =    0.050  
sample std dev ,    s =    5.8000  
Sample Size ,   n =    15  
Sample Mean,    x̅ =   36.4000  
          
degree of freedom=   DF=n-1=   14  
          
Standard Error , SE = s/√n =   5.8/√15=   1.4976  
t-test statistic= (x̅ - µ )/SE =    (36.4-32.6)/1.4976=   2.537  
          
critical t value, t* =    ±   2.1448   [Excel formula =t.inv(α/no. of tails,df) ]
          

Decision: |test stat| > |critical value | Reject null hypothesis   

  
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