Answer:
There is enough evidence to reject the manufacturer’s claim and the standardized test statistic z is -3.43
Step-by-step explanation:
A manufacturer of sprinkler systems designed for fire protection claims that the average activating temperature is at least 135°F.
So, Null hypothesis:[tex]H_0:\mu \geq 135[/tex]
Alternate hypothesis :[tex]H_a:\mu <135[/tex]
To test this claim, you randomly select a sample of 32 systems and find the mean activation temperature to be 133°F.
x=133
n = 32
Population Standard deviation =[tex]\sigma = 3.3^{\circ}F[/tex]
Formula :[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z=\frac{133-135}{\frac{3.3}{\sqrt{32}}}\\\\z=-3.428[/tex]
z=-3.43
Refer the z table for p value
p value = 0.0003
[tex]\alpha = 0.10[/tex]
p value < α
So, we failed to accept null hypothesis
Hence there is enough evidence to reject the manufacturer’s claim and the standardized test statistic z is -3.43