Keep getting test statistics and critical value wrong **Test the Claim****Objective:**Test the claim that the mean GPA of night students is larger than 3.4 at the 0.10 significance level.**Hypotheses:**The null and alternative hypotheses would be:1. \( H_0: \mu = 3.4 \) and \( H_1: \mu \neq 3.4 \) 2. \( H_0: \mu = 3.4 \) and \( H_1: \mu < 3.4 \)3. \( H_0: p = 0.85 \) and \( H_1: p < 0.85 \)4. \( H_0: p = 0.85 \) and \( H_1: p \neq 0.85 \) 5. \( H_0: \mu = 3.4 \) and \( H_1: \mu > 3.4 \) ✔6. \( H_0: p = 0.85 \) and \( H_1: p > 0.85 \)**Test Type:**The test is:- Two-tailed- Left-tailed- Right-tailed ✔Note: The correct hypotheses for this test are \( H_0: \mu = 3.4 \) and \( H_1: \mu > 3.4 \), and the test is a right-tailed test. ### Statistical Analysis of Sample GPA**Sample Size and Statistics:**- **Sample Size:** 75 people- **Sample Mean GPA:** 3.42- **Standard Deviation:** 0.04**Statistical Hypothesis Testing:**1. **Test Statistic Calculation:** - You will calculate the test statistic to two decimal places.2. **Critical Value Determination:** - Determine the critical value, also to two decimal places.3. **Hypothesis Decision:** - Based on the analysis, you should decide whether to: - Fail to reject the null hypothesis - Reject the null hypothesis - In this scenario, the conclusion was to "Reject the null hypothesis."This process involves determining whether the sample provides sufficient evidence to support a claim about the population mean, based on the calculated test statistic and critical value.

From the provided information, Sample size (n) = 75 Sample mean (x̅) = 3.42 Sample standard deviation (s) = 0.04The hypotheses are as follow: H0: µ = 3.4 H1: µ > 3.4 The test is right tailed. Level of significance (α) = 0.10 Since, the population standard deviation is unknown, therefore, the t distribution will be used. The value of the test statistic can be obtained as:The degree of freedom = n – 1 = 75 – 1 = 74 The critical value of t at 74 degree of freedom with 0.10 level of significance from the t value table is 1.29. Since, the test statistic value is greater than level of significance, therefore, the null hypothesis would reject. It can be concluded that there is sufficient evidence to support the claim that the mean GPA of night students is larger than 3.4.