Question

use technology and a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. assume the population is normally distributed. claim: μ>71; α=0.01 sample statistics: x̄=71.3, s=3.3, n=25 what are the null and alternative hypotheses? choose the correct answer below. a. h₀:μ≥71 hₐ:μ<71 b. h₀:μ≠71 hₐ:μ=71 c. h₀:μ≤71 hₐ:μ>71 d. h₀:μ=71 hₐ:μ≠71 what is the value of the standardized test statistic? the standardized test statistic is □. (round to two decimal places as needed.)

Explanation:

Step1: Calculate the standardized test statistic

The formula for the \(t -\)test statistic in a one - sample \(t -\)test (since the population standard deviation \(\sigma\) is unknown) is \(t=\frac{\bar{x}-\mu}{s/\sqrt{n}}\).
Here, \(\bar{x} = 71.3\), \(\mu = 71\) (from the null hypothesis \(H_0:\mu\leq71\)), \(s = 3.3\), and \(n = 25\).
Substitute the values into the formula: \(t=\frac{71.3 - 71}{3.3/\sqrt{25}}\).
First, calculate the denominator: \(s/\sqrt{n}=\frac{3.3}{5}=0.66\).
Then, calculate the numerator: \(\bar{x}-\mu=71.3 - 71 = 0.3\).
So, \(t=\frac{0.3}{0.66}\approx0.45\).

Answer:

The value of the standardized test statistic is \(0.45\).