Suppose you are testing The sample is large (n = 71) and the variance, σ2, is known. H0:μ=20 vs H1:μ>20. (a) Find the critical value(s) c

Question

Suppose you are testing The sample is large (n = 71) and the variance, σ2, is known. H0:μ=20 vs H1:μ>20. (a) Find the critical value(s) corresponding to α = 0.08. (b) You find that z = 1.56. Based on your critical value, what decision do you make regarding the null hypothesis (i.e. do you Reject H0 or Do Not Reject H0)?

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Delilah 4 days 2021-10-10T20:28:30+00:00 1 Answer 0

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    2021-10-10T20:30:14+00:00

    Answer:

    We reject the null hypothesis.

    Step-by-step explanation:

    We are given the following in the question:

    Sample size, n = 71

    Alpha, α = 0.08

    Population variance is known.

    First, we design the null and the alternate hypothesis

    H_{0}: \mu = 20\\H_A: \mu > 20

    We use One-tailed z test to perform this hypothesis.

    Formula:

    z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }

    a) We calculate the z-critical with the help of z-table.

    z_{critical} \text{ at 0.08 level of significance } = 1.41

    b)

    z_{stat} = 1.56

    Since,  

    z_{stat} > z_{critical}

    We fail to accept the null hypothesis and reject the null hypothesis and accept the alternate hypothesis.

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