g A manufacturer of sprinkler systems designed for fire protection claims that the average activating temperature is at least 135oF. To test

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.

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Margaret 1 week 2021-10-06T09:31:32+00:00 1 Answer 0

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    2021-10-06T09:32:47+00:00

    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 <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=\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

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