Use the sample data and significance level to test the claim that the population mean is 75. Sample data. x= 70, s= 4, n= 16. State the null hypothesis and the alternative hypothesis. Find the critical value, the test statistic , and state your conclusion about the claim. X = 0.01

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**Hypothesis Testing Using Sample Data**

**Objective:**

Use the sample data and significance level to test the claim that the population mean is 75.

**Sample Data:**

- Sample mean (\(\overline{x}\)): 70
- Sample standard deviation (\(s\)): 4
- Sample size (\(n\)): 16

**Instructions:**

1. **State the Null Hypothesis (\(H_0\))**: The population mean is 75.
2. **State the Alternative Hypothesis (\(H_a\))**: The population mean is not 75.
3. **Significance Level (\(\alpha\))**: 0.01
4. **Calculate**:
   - **Critical Value**: Based on the significance level and the test type.
   - **Test Statistic**: Use the formula for the test statistic appropriate for the data type (t-test or z-test).
5. **State your conclusion**: Determine whether to accept or reject the null hypothesis based on the test statistic and critical value.

This process helps in understanding the steps required for hypothesis testing using a given data set and significance level.
Transcribed Image Text:**Hypothesis Testing Using Sample Data** **Objective:** Use the sample data and significance level to test the claim that the population mean is 75. **Sample Data:** - Sample mean (\(\overline{x}\)): 70 - Sample standard deviation (\(s\)): 4 - Sample size (\(n\)): 16 **Instructions:** 1. **State the Null Hypothesis (\(H_0\))**: The population mean is 75. 2. **State the Alternative Hypothesis (\(H_a\))**: The population mean is not 75. 3. **Significance Level (\(\alpha\))**: 0.01 4. **Calculate**: - **Critical Value**: Based on the significance level and the test type. - **Test Statistic**: Use the formula for the test statistic appropriate for the data type (t-test or z-test). 5. **State your conclusion**: Determine whether to accept or reject the null hypothesis based on the test statistic and critical value. This process helps in understanding the steps required for hypothesis testing using a given data set and significance level.
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