Questions: A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500 so they provide additional training on use of the form. Previously the average time spent on the form was 6.3 hours.
After the training, in order to test whether the time to fill out the form has been reduced, a sample of 48 small business owners who annually complete the form was randomly chosen, and their completion times recorded. The mean completion time for ABC-5500 form was 5.7 hours with a standard deviation of 1.8 hours.
In order to test that the time to complete the form has been reduced, state the appropriate null and alternative hypotheses.
H0: μ=6.3
H3: μ<6.3
H0: μ=6.3
H3: μ ≠ 6.3
H0: μ>6.3
H3: μ<6.3
H0: μ=6.3
H3: μ>6.3
Transcript text: A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500 so they provide additional training on use of the form. Previously the average time spent on the form was 6.3 hours.
After the training, in order to test whether the time to fill out the form has been reduced, a sample of 48 small business owners who annually complete the form was randomly chosen, and their completion times recorded. The mean completion time for ABC-5500 form was 5.7 hours with a standard deviation of 1.8 hours.
In order to test that the time to complete the form has been reduced, state the appropriate null and alternative hypotheses.
$H_{0}: \mu=6.3$
$H_{3}: \mu<6.3$
$H_{0}: \mu=6.3$
$H_{3}: \mu \neq 6.3$
$H_{0}: \mu>6.3$
$H_{3}: \mu<6.3$
\[
\begin{array}{l}
H_{0}: \mu=6.3 \\
H_{3}: \mu>6.3
\end{array}
\]
Solution
Solution Steps
Step 1: Identify the problem
The problem involves testing whether the average time to complete the ABC-5500 form has been reduced after additional training. The previous average time was 6.3 hours, and a sample of 48 small business owners showed a mean completion time of 5.7 hours with a standard deviation of 1.8 hours.
Step 2: State the null hypothesis
The null hypothesis \( H_0 \) represents the status quo, which is that the average time to complete the form has not changed. Therefore:
\[
H_0: \mu = 6.3
\]
Step 3: State the alternative hypothesis
The alternative hypothesis \( H_a \) represents the claim that the average time to complete the form has been reduced. Therefore:
\[
H_a: \mu < 6.3
\]