find the standardized test statistic t for a sample with n = 25, x = 20, s = 3, and α = 0.005 if h_a: μ 19. round your answer to two decimal places. a. 2.00 b. 1.45 c. 1.24 d. 1.67

Question

find the standardized test statistic t for a sample with n = 25,  x = 20, s = 3, and α = 0.005 if h_a: μ > 19. round your answer to two decimal places. a. 2.00 b. 1.45 c. 1.24 d. 1.67

Accepted Answer

# Explanation:
## Step1: Recall the formula for the t - statistic
The formula for the t - statistic in a one - sample t - test is $t=\frac{\bar{x}-\mu}{s/\sqrt{n}}$

## Step2: Identify the values of $\bar{x}$, $\mu$, $s$, and $n$
Given $\bar{x} = 20$, $\mu=19$ (from the null hypothesis $H_{0}$ related to the alternative $H_{a}:\mu>19$), $s = 3$, and $n=25$

## Step3: Substitute the values into the formula
$$
\begin{align*}
t&=\frac{20 - 19}{3/\sqrt{25}}\
&=\frac{1}{3/5}\
&=\frac{1}{\frac{3}{5}}\
&=\frac{5}{3}\approx1.67
\end{align*}
$$

# Answer:
D. 1.67

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the t - statistic

Step2: Identify the values of \(\bar{x}\), \(\mu\), \(s\), and \(n\)

Step3: Substitute the values into the formula

Answer: