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

There is enough evidence to reject the manufacturer’s claim and the standardized test statistic z is -3.43

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 <135`

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=(x-\mu)/((\sigma)/(√(n)))`

`z=(133-135)/((3.3)/(√(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