Answer: -1.51
Step-by-step explanation:
Let [tex]\mu[/tex] be the population mean rating of car.
As per given , we have
[tex]H_0: \mu=42.8[/tex]
[tex]H_a: \mu\neq42.8[/tex]
Since population variance is known, so we use z-test.
Test statistic : [tex]z=\dfrac{\overline{x}-\mu}{\sqrt{\dfrac{\sigma^2}{n}}}[/tex]
, where n= sample size
[tex]\overline{x}[/tex] = Sample mean
[tex]\sigma^2[/tex]= variance
As per given ,
n=300
[tex]\overline{x}=42.6[/tex]
[tex]\sigma^2=5.29[/tex]
[tex]\mu=42.8[/tex]
Put these values in formula we get
[tex]z=\dfrac{42.6-42.8}{\sqrt{\dfrac{5.29}{300}}}[/tex]
[tex]z=\dfrac{-0.2}{\sqrt{0.0176333}}[/tex]
[tex]z=\dfrac{-0.2}{0.13279}=-1.50613751035\approx1.51[/tex]
Hence, the value of the test statistic is z= -1.51 .
