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 □. (round to two decimal places as needed.)

Explanation:

Step1: Recall the formula for the z - test statistic

The formula for the z - test statistic when the population standard deviation \(\sigma\) is known is \(z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\)

Step2: Identify the values of \(\bar{x}\), \(\mu\), \(\sigma\), and \(n\)

We are given that \(\bar{x} = 6300\), \(\mu=6000\), \(\sigma = 407\), and \(n = 38\)

Step3: Substitute the values into the formula

$$
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$$

First, calculate \(\sqrt{38}\approx6.1644\), then \(\frac{407}{6.1644}\approx66.02\)

$$ z=\frac{300}{66.02}\approx4.54 $$

Answer:

\(4.54\)