MATH1127: Introduction to Statistics (60022)
... Lesson 9.3 Distribution Needed for Hypothesis Testing
score: $4 L / 100 \quad 6 / 14$ answered
Question 12
Testing:
\[
\begin{array}{r}
H_{0}: \mu \geq 13.9 \\
H_{1}: \mu< 13.9
\end{array}
\]
Your sample consists of 20 values, with a sample mean of 13.6. Suppose the population standard deviation is known to be 1.5 .
a) Calculate the value of the test statistic, rounded to 2 decimal places.
\[
z=
\]
b) At $\alpha=0.02$, the rejection region is
\[
\begin{array}{l}
z> 2.05 \\
z> 2.33 \\
z< -2.05 \\
z< -2.33 \\
z< -2.05 \text { or } z> 2.05 \\
z< -2.33 \text { or } z> 2.33
\end{array}
\]
c) The decision is to
Accept the null hypothesis
Accept the alternative hypotheis
IIM 2842.jpg
IMG 2841.jpg
MG $2840 . j p g$
Answer
Solving the above expression, we find that the value of the test statistic, rounded to 2 decimal places, is \(\boxed{-0.89}\)
Step 1 ：Given that the population mean (mu) is 13.9, the sample mean (x_bar) is 13.6, the population standard deviation (sigma) is 1.5, and the sample size (n) is 20.
Step 2 ：We calculate the test statistic (z) using the formula: \(z = \frac{x_{bar} - \mu}{\frac{\sigma}{\sqrt{n}}}\)
Step 3 ：Substituting the given values into the formula, we get: \(z = \frac{13.6 - 13.9}{\frac{1.5}{\sqrt{20}}}\)
Step 4 ：Solving the above expression, we find that the value of the test statistic, rounded to 2 decimal places, is \(\boxed{-0.89}\)
