Question

a sample mean, sample size, and sample standard deviation are provided below. use the one - mean t - test to perform the required hypothesis test at the 10% significance level.

x = 25, s = 7, n = 15, h₀: μ = 30, hₐ: μ ≠ 30

click here to view a partial table of values of tₐ.

the test statistic is t =
(round to two decimal places as needed.)

Explanation:

Step1: Recall the formula for the t - statistic

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

Step2: Substitute the given values into the formula

We are given \(\bar{x} = 25\), \(\mu=30\), \(s = 7\), and \(n = 15\).
First, calculate \(s/\sqrt{n}\): \(\frac{s}{\sqrt{n}}=\frac{7}{\sqrt{15}}\approx\frac{7}{3.87298}\approx1.807\)
Then, calculate \(\bar{x}-\mu\): \(25 - 30=- 5\)
Now, find \(t\): \(t=\frac{25 - 30}{7/\sqrt{15}}=\frac{-5}{7/\sqrt{15}}\)

$$t=\frac{-5\sqrt{15}}{7}\approx\frac{-5\times3.87298}{7}\approx\frac{-19.3649}{7}\approx - 2.77$$

Answer:

\(-2.77\)