Question 1180574: State the null hypothesis and the alternative hypothesis in (a) words and in
(b) symbols for each of the following.
a. A librarian of a school claims that all their grade 8 students read an
average of 10 storybooks a month with a standard deviation of 2 books.
A random sample of grade 8 students read an average 12 books a month
and a standard deviation of 1 book. The confidence statement is 95%.
b. According to a factory employer, the mean working time of workers in
the factory is 6 hours with a standard deviation of 0.5 hours. A
researcher interviewed 50% of the employees and found out that their
mean working time is 8 hours with a standard deviation of 1 hour. The a
level is 0.05.
Sketch the graph of each null and alternative hypothesis (one-tailed test and two-tailed test)
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's the breakdown of null and alternative hypotheses, both in words and symbols, along with sketches of their graphs:
**a. Librarian's Claim:**
The librarian claims the average number of storybooks read by Grade 8 students is 10. The sample shows an average of 12. We'll consider both one-tailed (right-tailed) and two-tailed tests.
**(a) Hypotheses:**
**One-Tailed (Right-Tailed):**
* **H0 (Words):** The average number of storybooks read by Grade 8 students is equal to 10.
* **H1 (Words):** The average number of storybooks read by Grade 8 students is greater than 10.
* **H0 (Symbols):** μ = 10
* **H1 (Symbols):** μ > 10
**Two-Tailed:**
* **H0 (Words):** The average number of storybooks read by Grade 8 students is equal to 10.
* **H1 (Words):** The average number of storybooks read by Grade 8 students is *not* equal to 10.
* **H0 (Symbols):** μ = 10
* **H1 (Symbols):** μ ≠ 10
**(b) Graphs:**
**One-Tailed (Right-Tailed):**
```
H0: μ = 10 H1: μ > 10
--------------------- ---------------------
| | | / |
| | | / |
| / | | / |
| / | | / |
| / | | / |
| / | | / |
| / | | / |
| / | | / |
| / | |/ |
--------------------- ---------------------
10 x̄ 10 x̄
```
**Two-Tailed:**
```
H0: μ = 10 H1: μ ≠ 10
--------------------- ---------------------
| / | | / \ |
| / | | / \ |
| / | | / \ |
| / | | / \ |
| / | | / \ |
| / | | / \ |
| / | |/ \ |
| / | | \ |
|/ | | \ |
--------------------- ---------------------
10 x̄ 10 x̄
```
**b. Factory Employer's Claim:**
The employer claims the mean working time is 6 hours. The researcher found a mean of 8 hours. We'll consider both one-tailed (right-tailed) and two-tailed tests.
**(a) Hypotheses:**
**One-Tailed (Right-Tailed):**
* **H0 (Words):** The mean working time is equal to 6 hours.
* **H1 (Words):** The mean working time is greater than 6 hours.
* **H0 (Symbols):** μ = 6
* **H1 (Symbols):** μ > 6
**Two-Tailed:**
* **H0 (Words):** The mean working time is equal to 6 hours.
* **H1 (Words):** The mean working time is *not* equal to 6 hours.
* **H0 (Symbols):** μ = 6
* **H1 (Symbols):** μ ≠ 6
**(b) Graphs:**
**One-Tailed (Right-Tailed):**
```
H0: μ = 6 H1: μ > 6
--------------------- ---------------------
| | | / |
| | | / |
| / | | / |
| / | | / |
| / | | / |
| / | | / |
| / | | / |
| / | | / |
| / | |/ |
--------------------- ---------------------
6 x̄ 6 x̄
```
**Two-Tailed:**
```
H0: μ = 6 H1: μ ≠ 6
--------------------- ---------------------
| / | | / \ |
| / | | / \ |
| / | | / \ |
| / | | / \ |
| / | | / \ |
| / | | / \ |
| / | |/ \ |
| / | | \ |
|/ | | \ |
--------------------- ---------------------
6 x̄ 6 x̄
```
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