A data set includes weights​ (in grams) of 33 ​Reese's Peanut Butter Cup Miniatures. The accompanying Statdisk display shows results from using all 33 weights to test the claim that the sample is from a population with a mean equal to 8.953 g. Test the given claim by using the display provided from Statdisk. Use a 0.05 significance level.

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A data set includes weights​ (in grams) of 33 ​Reese's Peanut Butter Cup Miniatures. The accompanying Statdisk display shows results from using all 33 weights to test the claim that the sample is from a population with a mean equal to 8.953 g. Test the given claim by using the display provided from Statdisk. Use a 0.05 significance level.
**Identify the null and alternative hypotheses.**

- \( H_0: \) [Dropdown for choosing mathematical signs: =, <, >] [Box for entering value]
- \( H_1: \) [Dropdown for choosing mathematical signs: =, <, >] [Box for entering value]

*(Type integers or decimals. Do not round.)*

**Identify the test statistic.**

- [Box for entering the test statistic value]

*(Round to two decimal places as needed.)*

**Identify the P-value.**

- [Box for entering the P-value]

*(Round to three decimal places as needed.)*

**State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.**

- [Dropdown: Reject/Fail to reject] the null hypothesis. There [Dropdown: is/is not] sufficient evidence at the 0.10 significance level to [Dropdown: support/refute] the claim that the sample is from a population with a mean systolic blood pressure level greater than 120 mm Hg.
Transcribed Image Text:**Identify the null and alternative hypotheses.** - \( H_0: \) [Dropdown for choosing mathematical signs: =, <, >] [Box for entering value] - \( H_1: \) [Dropdown for choosing mathematical signs: =, <, >] [Box for entering value] *(Type integers or decimals. Do not round.)* **Identify the test statistic.** - [Box for entering the test statistic value] *(Round to two decimal places as needed.)* **Identify the P-value.** - [Box for entering the P-value] *(Round to three decimal places as needed.)* **State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.** - [Dropdown: Reject/Fail to reject] the null hypothesis. There [Dropdown: is/is not] sufficient evidence at the 0.10 significance level to [Dropdown: support/refute] the claim that the sample is from a population with a mean systolic blood pressure level greater than 120 mm Hg.
### Educational Website Content: Statistical Analysis of Reese's Peanut Butter Cup Miniatures

A data set includes weights (in grams) of 33 Reese's Peanut Butter Cup Miniatures. The accompanying Statdisk display shows results from using all 33 weights to test the claim that the sample is from a population with a mean equal to 8.953 g. Test the given claim by using the display provided from Statdisk, using a 0.05 significance level.

#### Steps for Analysis:

1. **Identify the null and alternative hypotheses:**
   - \( H_0: \) The population mean is equal to 8.953 g.
   - \( H_1: \) The population mean is not equal to 8.953 g.

2. **Statistical Test Information:**
   - **Test Type:** t Test
   - **Test Statistic, t:** -3.89274
   - **Critical t:** ±2.03693
   - **P-value:** 0.00047

#### Interpretation:

- **Null Hypothesis (\( H_0 \)):** The assumption that the sample comes from a population with a mean weight equal to 8.953 grams.

- **Alternative Hypothesis (\( H_1 \)):** The assumption that the sample comes from a population with a mean weight not equal to 8.953 grams.

- **Test Statistic:** A t-value of -3.89274 was calculated, which measures the difference between the sample mean and the population mean in terms of standard deviation units.

- **Critical t-value:** The threshold values (±2.03693) determine the boundaries for rejecting the null hypothesis at the 0.05 significance level.

- **P-value:** With a p-value of 0.00047, which is less than the significance level of 0.05, the null hypothesis is rejected, indicating that the sample mean is significantly different from the population mean.

#### Conclusion:
Given the test results, there is strong evidence to reject the null hypothesis. Therefore, it is likely that the sample comes from a population with a mean weight that is not equal to 8.953 grams.
Transcribed Image Text:### Educational Website Content: Statistical Analysis of Reese's Peanut Butter Cup Miniatures A data set includes weights (in grams) of 33 Reese's Peanut Butter Cup Miniatures. The accompanying Statdisk display shows results from using all 33 weights to test the claim that the sample is from a population with a mean equal to 8.953 g. Test the given claim by using the display provided from Statdisk, using a 0.05 significance level. #### Steps for Analysis: 1. **Identify the null and alternative hypotheses:** - \( H_0: \) The population mean is equal to 8.953 g. - \( H_1: \) The population mean is not equal to 8.953 g. 2. **Statistical Test Information:** - **Test Type:** t Test - **Test Statistic, t:** -3.89274 - **Critical t:** ±2.03693 - **P-value:** 0.00047 #### Interpretation: - **Null Hypothesis (\( H_0 \)):** The assumption that the sample comes from a population with a mean weight equal to 8.953 grams. - **Alternative Hypothesis (\( H_1 \)):** The assumption that the sample comes from a population with a mean weight not equal to 8.953 grams. - **Test Statistic:** A t-value of -3.89274 was calculated, which measures the difference between the sample mean and the population mean in terms of standard deviation units. - **Critical t-value:** The threshold values (±2.03693) determine the boundaries for rejecting the null hypothesis at the 0.05 significance level. - **P-value:** With a p-value of 0.00047, which is less than the significance level of 0.05, the null hypothesis is rejected, indicating that the sample mean is significantly different from the population mean. #### Conclusion: Given the test results, there is strong evidence to reject the null hypothesis. Therefore, it is likely that the sample comes from a population with a mean weight that is not equal to 8.953 grams.
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