Question

use 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 ≥ 7900; α = 0.10 sample statistics: (overline{x}=7600), s = 440, n = 20
what are the null and alternative hypotheses?
a. (h_{0}:mu
eq7900)
(h_{a}:mu = 7900)
b. (h_{0}:muleq7900)
(h_{a}:mu>7900)
c. (h_{0}:mu = 7900)
(h_{a}:mu
eq7900)
d. (h_{0}:mugeq7900)
(h_{a}:mu<7900)
what is the value of the standardized test statistic?
the standardized test statistic is (square). (round to two decimal places as needed.)

Explanation:

Step1: Recall the formula for the t - test statistic

The formula for the t - test statistic is \(t=\frac{\bar{x}-\mu}{s/\sqrt{n}}\), where \(\bar{x}\) is the sample mean, \(\mu\) is the population mean under the null hypothesis, \(s\) is the sample standard deviation, and \(n\) is the sample size.

Step2: Identify the values from the problem

We are given \(\bar{x} = 7600\), \(\mu = 7900\) (from the claim \(\mu\geq7900\), under the null hypothesis \(H_0:\mu\geq7900\), we use \(\mu = 7900\) for calculation), \(s = 440\), and \(n = 20\).

Step3: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Answer:

The standardized test statistic is \(-3.05\)