Question A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally d

Question

Question
A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed, with standard deviation 0.25 Volts, and the manufacturer wishes to test H0: μ = 5 Volts against H1: μ ≠ 5 Volts, using n = 8 units. If the sample mean is x¯¯=4.85 what can you say about the population mean with a=0.05 significance level ?

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Ella 1 week 2021-09-12T13:22:33+00:00 1 Answer 0

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    2021-09-12T13:23:53+00:00

    Answer:

    The population mean is 5 volts

    Step-by-step explanation:

    Output voltage is assumed to be normally distributed, with standard deviation 0.25 Volts

    s=0.25

    n = 8

    H_0:\mu = 5\\H_a:\mu \neq 5

    Sample mean = \bar{x}=4.85

    Since n < 30 and population standard deviation is unknown

    So, we will use t test

    Formula : t = \frac{x-\mu}{\frac{s}{\sqrt{n}}}

    t = \frac{4.85-5}{\frac{0.25}{\sqrt{8}}}

    t=-1.69

    Refer the t table for p value

    Degree of freedom = n-1 = 8-1 = 7

    So,t_{(df,\alpha)}=t_{7,0.05}=2.365

    P value >α

    So, We are failed to reject null hypothesis

    Hence The population mean is 5 volts

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