Question 1180574
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
```