Question

test the claim about the population mean, μ, at the given level of significance using the given sample statistics. claim: μ = 50; α = 0.02; σ = 3.73. sample statistics: ˉx = 48.6, n = 77 identify the null and alternative hypotheses. choose the correct answer below. a. h₀: μ = 50 hₐ: μ > 50 b. h₀: μ = 50 hₐ: μ < 50 c. h₀: μ = 50 hₐ: μ ≠ 50 d. h₀: μ < 50 hₐ: μ = 50 e. h₀: μ > 50 hₐ: μ = 50 f. h₀: μ ≠ 50 hₐ: μ = 50 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: Substitute the given values into the formula

We are given \(\bar{x} = 48.6\), \(\mu=50\), \(\sigma = 3.73\), and \(n = 77\)

First, calculate \(\frac{\sigma}{\sqrt{n}}=\frac{3.73}{\sqrt{77}}\approx\frac{3.73}{8.775}\approx0.425\)

Then, \(z=\frac{48.6 - 50}{0.425}=\frac{- 1.4}{0.425}\approx - 3.29\)

Answer:

\(-3.29\)