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 5% significance level.
$overline{x}=25$, $s = 7$, $n = 32$, $h_0:mu=28$, $h_a:mult28$
click here to view a partial table of values of $t_2$.
the test statistic is $t=square$
(round to two decimal places as needed.)

Explanation:

Step1: Recall the formula for the one - mean t - test statistic

The formula for the one - mean t - test statistic is \(t=\frac{\bar{x}-\mu_0}{s/\sqrt{n}}\), where \(\bar{x}\) is the sample mean, \(\mu_0\) 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

Given \(\bar{x} = 25\), \(\mu_0=28\), \(s = 7\), and \(n = 32\).
First, calculate \(s/\sqrt{n}\): \(\frac{s}{\sqrt{n}}=\frac{7}{\sqrt{32}}\approx\frac{7}{5.65685}\approx1.237\).
Then, calculate \(t\): \(t=\frac{25 - 28}{7/\sqrt{32}}=\frac{- 3}{7/\sqrt{32}}\).
Since \(\frac{-3}{7/\sqrt{32}}=-3\times\frac{\sqrt{32}}{7}\approx-3\times\frac{5.65685}{7}\).
\(t\approx - 2.42\)

Answer:

\(-2.42\)