Test the claim that the mean GPA of night students is larger than 3.1 at the .005 significance level. The null and alternative hypothesis would be: Ho:p = 0.775 Ho:p= 0.775 Ho: H1:p> 0.775 H1:p< 0.775 H1:µ# 3.1 H1:µ < 3.1 H1:µ > 3.1 H¡ :p+ 0.775 / 3.1 Ho: u = 3.1 Ho:µ = 3.1 Ho:p = 0.775 o The test is: right-tailed left-tailed two-tailed o Based on a sample of 55 people, the sample mean GPA was 3.15 with a standard deviation of 0.05 The test statistic is: (to 2 decimals) The critical value is: (to 2 decimals) Based on this we: O Reject the null hypothesis O Fail to reject the null hypothesis

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### Hypothesis Testing Example

**Problem Statement:**
Test the claim that the mean GPA of night students is larger than 3.1 at the 0.005 significance level.

**Null and Alternative Hypothesis:**
\[ 
\begin{aligned}
H_0: & \ \mu \leq 3.1 \\
H_1: & \ \mu > 3.1 \\
\end{aligned}
\]

**Test Type:**
Right-tailed

*Right-tailed option is selected*

**Sample Data:**
- Sample size: 55
- Sample mean GPA: 3.15
- Standard deviation: 0.05

**Calculations:**
1. **Test Statistic (to 2 decimals):**
   \[ \text{Test statistic: } \_\_\_\_ \]

   *Calculations need to be performed and filled in.*

2. **Critical Value (to 2 decimals):**
   \[ \text{Critical value: } \_\_\_\_ \]

   *Calculations need to be performed and filled in.*

**Decision:**
Based on this we:

- [X] Reject the null hypothesis
- [ ] Fail to reject the null hypothesis

**Summary:**
The test statistic and corresponding critical value need to be calculated to make an informed decision. However, based on the sample data provided, we reject the null hypothesis, indicating that there is sufficient evidence to support the claim that the mean GPA of night students is greater than 3.1 at the 0.005 significance level.
Transcribed Image Text:### Hypothesis Testing Example **Problem Statement:** Test the claim that the mean GPA of night students is larger than 3.1 at the 0.005 significance level. **Null and Alternative Hypothesis:** \[ \begin{aligned} H_0: & \ \mu \leq 3.1 \\ H_1: & \ \mu > 3.1 \\ \end{aligned} \] **Test Type:** Right-tailed *Right-tailed option is selected* **Sample Data:** - Sample size: 55 - Sample mean GPA: 3.15 - Standard deviation: 0.05 **Calculations:** 1. **Test Statistic (to 2 decimals):** \[ \text{Test statistic: } \_\_\_\_ \] *Calculations need to be performed and filled in.* 2. **Critical Value (to 2 decimals):** \[ \text{Critical value: } \_\_\_\_ \] *Calculations need to be performed and filled in.* **Decision:** Based on this we: - [X] Reject the null hypothesis - [ ] Fail to reject the null hypothesis **Summary:** The test statistic and corresponding critical value need to be calculated to make an informed decision. However, based on the sample data provided, we reject the null hypothesis, indicating that there is sufficient evidence to support the claim that the mean GPA of night students is greater than 3.1 at the 0.005 significance level.
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