Question

test the claim about the population mean, μ, at the given level of significance using the given sample statistics. claim: μ≠6000; α=0.09; σ=407. sample statistics: x̄=6300, n=38 identify the null and alternative hypotheses. choose the correct answer below. a. h₀: μ≥6000 hₐ: μ≠6000 b. h₀: μ≠6000 hₐ: μ≥6000 c. h₀: μ≤6000 hₐ: μ≠6000 d. h₀: μ≠6000 hₐ: μ=6000 e. h₀: μ≠6000 hₐ: μ≤6000 f. h₀: μ=6000 hₐ: μ≠6000 calculate the standardized test statistic. the standardized test statistic is 4.54 (round to two decimal places as needed.) determine the critical value(s). select the correct choice below and fill in the answer box to complete your choice. (round to two decimal places as needed.) a. the critical value is b. the critical values are ±

Explanation:

Step1: Determine the type of test

Since the claim is \(\mu
eq6000\), this is a two - tailed test. For a two - tailed test with significance level \(\alpha = 0.09\), the area in each tail is \(\frac{\alpha}{2}=\frac{0.09}{2}=0.045\).

Step2: Find the critical values

We use the standard normal distribution \(z\). We look for the \(z\) - values such that \(P(Z < -z_{c})=0.045\) and \(P(Z>z_{c}) = 0.045\). Using a standard normal table or a calculator, the \(z\) - value corresponding to an area of \(1 - 0.045=0.955\) is \(z_{c}\approx1.70\) (because \(P(Z < 1.70)=0.9554\) and \(P(Z<- 1.70)=0.0446\approx0.045\)).

Answer:

B. The critical values are \(\pm1.70\)