find the standardized test statistic t for a sample with ( n = 20 ), ( overline{x}=10.7 ), ( s = 2.0 ), and ( alpha = 0.05 ) if ( h_{a}:mu

Question

find the standardized test statistic t for a sample with ( n = 20 ), ( overline{x}=10.7 ), ( s = 2.0 ), and ( alpha = 0.05 ) if ( h_{a}:mu<11.1 ). round your answer to two decimal places.
a. ( -0.89 )
b. ( -0.87 )
c. ( -1.27 )
d. ( -1.23 )

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
We are given that $\bar{x} = 10.7$, $\mu=11.1$, $s = 2.0$, and $n = 20$

## Step3: Substitute the values into the formula
$$
\begin{align*}
t&=\frac{10.7 - 11.1}{2.0/\sqrt{20}}\
&=\frac{- 0.4}{2.0/4.472}\
&=\frac{-0.4}{0.4472}\
&\approx - 0.89
\end{align*}
$$

# Answer:
A. - 0.89

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the t - statistic

Step2: Identify the values

Step3: Substitute the values into the formula

Answer: