Question

g A manufacturer of sprinkler systems designed for fire protection claims that the average activating temperature is at least 135oF. To test this claim, you randomly select a sample of 32 systems and find the mean activation temperature to be 133oF. Assume the population standard deviation is 3.3oF. At alpha = 0.10, do you have enough evidence to reject the manufacturer's claim? Find the standardized test statistic z. Round your answer to the hundredths place.

Answer 1

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:$H_0:\mu \geq 135$

Alternate hypothesis :$H_a:\mu$

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 =$\sigma = 3.3^{\circ}F$

Formula :$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

$z=\frac{133-135}{\frac{3.3}{\sqrt{32}}}\\\\z=-3.428$

z=-3.43

Refer the z table for p value

p value = 0.0003

$\alpha = 0.10$

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