Question

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?

Answer #1

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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