find the standardized test statistic ( t ) for a sample with ( n = 25, overline{x}=72, s = 3 ), and ( alpha = 0.10 ) if ( h_{a}: mu71 ). round your answer to two decimal places.
oa. 1.24
ob. 1.45
oc. 2.00
od. 1.67

Question

find the standardized test statistic ( t ) for a sample with ( n = 25, overline{x}=72, s = 3 ), and ( alpha = 0.10 ) if ( h_{a}: mu>71 ). round your answer to two decimal places.
oa. 1.24
ob. 1.45
oc. 2.00
od. 1.67

Accepted Answer

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

## Step2: Identify the values of $\bar{x},\mu,s,n$
Given $\bar{x} = 72$, $\mu = 71$ (from $H_{a}:\mu>71$), $s = 3$, $n = 25$

## Step3: Substitute the values into the formula
$$
\begin{align*}
t&=\frac{72 - 71}{3/\sqrt{25}}\
&=\frac{1}{3/5}\
&=\frac{5}{3}\approx1.67
\end{align*}
$$

# Answer:
D. $1.67$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the \(t -\)test statistic

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

Step3: Substitute the values into the formula

Answer: