Suppose the span of thin iPhones has a population that is normally distributed with a standard deviation of 10. I sample 96 thin iPhones from this population and obtain a mean span of 58.81 and a standard deviation of 10.756. Using an alpha value of α = 0.05, is this observed mean significantly less than an expected span of 59?
|null hypothesis:Ho μ||=||59|
|Alternate Hypothesis:Ha μ||<||59|
|for 0.05 level with left tail test , critical z=||-1.645||(from excel:normsinv(0.05)|
|Decision rule:reject Ho if test statistic z<-1.645|
|population mean μ=||59|
|sample mean 'x̄=||58.810|
|sample size n=||96|
|std deviation σ=||10.00|
|std error ='σx=σ/√n=10/√96=||1.0206|
|z statistic= ='(x̄-μ)/σx=(58.81-59)/1.021=||-0.19|
|p value =||0.4247||(from excel:1*normsdist(-0.19)|
|since test statistic does not falls in rejection region we fail to reject null hypothesis|
|we do not have have sufficient evidence to conclude that observed mean is significantly less than an expected span of 59|
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