The lifespan of xenon metal halide arcdischarge bulbs for ai

The lifespan of xenon metal halide arc-discharge bulbs for aircraft landing lights is normally distributed with a mean of 1.900 hours and a standard deviation of 580 hours. (a) If a new ballast system shows a mean life of 2,316 hours in a test on a sample of 13 prototype new bulbs, would you conclude that the new lamp?s mean life exceeds the current mean life at alpha = 0.10? No Yes (b) What is the p-value? (Round your answers to 4 decimal places.) p-value

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   1900  
Ha:    u   <   1900  
              
As we can see, this is a    1   tailed test.      
              
Thus, getting the critical z, as alpha =    0.1   ,      
              
zcrit =    1.281551566          
              
Getting the test statistic, as              
              
X = sample mean =    2316          
uo = hypothesized mean =    1900          
n = sample size =    13          
s = standard deviation =    580          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.58605057          
              
Also, the p value is              
              
p =    0.004854134  
              
Comparing z and zcrit (or, p and significance level), we   REJECT THE NULL HYPOTHESIS.

[ANSWER IS YES: We conclude that it exceeds 1900. YES.]

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As earlier,

p =    0.004854134   [answer, part b]