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: x̄ = 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 - 3.29 (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 alternative hypothesis \(H_{a}:\mu
eq50\), this is a two - tailed test.

Step2: Find the critical values

For a two - tailed test with \(\alpha = 0.02\), the significance level in each tail is \(\frac{\alpha}{2}=0.01\).
Using the standard normal distribution \(z\) - table (or a calculator with a normal distribution function), the critical values are \(z_{\alpha/2}\) and \(-z_{\alpha/2}\).
Looking up the \(z\) - value corresponding to an area of \(1 - 0.01=0.99\) in the right - tail of the standard normal distribution, we find \(z_{0.01}\approx2.33\).

Answer:

B. The critical values are \(\pm2.33\)