Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value =
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value =
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
q7
![**Calculating the Test Statistic and Determining the P-value**
To determine the significance of a hypothesis test, it is important to calculate the test statistic and the associated P-value. Follow the instructions below to complete this process:
1. **Calculate the Test Statistic (z):**
- Use the appropriate formula based on your test type (e.g., z-test, t-test).
- Round your test statistic value to two decimal places.
2. **Determine the P-value:**
- Once the test statistic is calculated, use statistical tables or software to find the P-value.
- Round your P-value to four decimal places.
**Input Fields:**
- **z = [ ]**
- **P-value = [ ]**
**Instructions for Rounding:**
- The test statistic (z) should be rounded to two decimal places.
- The P-value should be rounded to four decimal places.
These precise calculations will help in making a decision regarding the null hypothesis. If you have any questions or need further assistance, refer to the resources provided on z-test and P-value calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18694516-cac0-450c-bfd2-4a4488b9c5fd%2F337cffc0-4cf0-4d24-9e76-84f9f0450436%2Fj9x903_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculating the Test Statistic and Determining the P-value**
To determine the significance of a hypothesis test, it is important to calculate the test statistic and the associated P-value. Follow the instructions below to complete this process:
1. **Calculate the Test Statistic (z):**
- Use the appropriate formula based on your test type (e.g., z-test, t-test).
- Round your test statistic value to two decimal places.
2. **Determine the P-value:**
- Once the test statistic is calculated, use statistical tables or software to find the P-value.
- Round your P-value to four decimal places.
**Input Fields:**
- **z = [ ]**
- **P-value = [ ]**
**Instructions for Rounding:**
- The test statistic (z) should be rounded to two decimal places.
- The P-value should be rounded to four decimal places.
These precise calculations will help in making a decision regarding the null hypothesis. If you have any questions or need further assistance, refer to the resources provided on z-test and P-value calculations.
![**Statistical Hypothesis Testing: Calorie Estimates for Alcoholic Beverages**
Unlike most packaged food products, alcoholic beverage container labels are not required to show calorie or nutrient content. An article reports on a pilot study where each of 56 individuals in a sample was asked to estimate the calorie content of a 12 oz can of beer known to contain 153 calories. The resulting sample mean estimated calorie level was 193, and the sample standard deviation was 88.
**Research Question:** Does this data suggest that the true average estimated calorie content in the population sampled exceeds the actual content?
**Hypothesis Testing:**
We'll test the appropriate hypotheses at a significance level of 0.001.
1. **Null Hypothesis (H₀):** The true average estimated calorie content is equal to the actual calorie content. (\(\mu = 153\))
2. **Alternative Hypothesis (H₁):** The true average estimated calorie content exceeds the actual calorie content. (\(\mu > 153\))
This involves conducting a one-sample t-test given the following data:
- Sample Size \( n = 56 \)
- Sample Mean \( \bar{x} = 193 \)
- Population Mean \( \mu = 153 \)
- Sample Standard Deviation \( s = 88 \)
- Significance Level \( \alpha = 0.001 \)
To perform this test:
- Calculate the t-score using the formula: \[ t = \frac{\bar{x} - \mu}{s/\sqrt{n}} \]
- Compare the calculated t-score with the critical t-value from the t-distribution table at 55 degrees of freedom (n-1) for a one-tailed test at the 0.001 significance level.
An appropriate conclusion would be drawn based on whether the t-score exceeds the critical t-value.
This evaluation will help determine if there is a statistically significant overestimation of calorie content in the sample population.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18694516-cac0-450c-bfd2-4a4488b9c5fd%2F337cffc0-4cf0-4d24-9e76-84f9f0450436%2Fmgs9l3t_processed.png&w=3840&q=75)
Transcribed Image Text:**Statistical Hypothesis Testing: Calorie Estimates for Alcoholic Beverages**
Unlike most packaged food products, alcoholic beverage container labels are not required to show calorie or nutrient content. An article reports on a pilot study where each of 56 individuals in a sample was asked to estimate the calorie content of a 12 oz can of beer known to contain 153 calories. The resulting sample mean estimated calorie level was 193, and the sample standard deviation was 88.
**Research Question:** Does this data suggest that the true average estimated calorie content in the population sampled exceeds the actual content?
**Hypothesis Testing:**
We'll test the appropriate hypotheses at a significance level of 0.001.
1. **Null Hypothesis (H₀):** The true average estimated calorie content is equal to the actual calorie content. (\(\mu = 153\))
2. **Alternative Hypothesis (H₁):** The true average estimated calorie content exceeds the actual calorie content. (\(\mu > 153\))
This involves conducting a one-sample t-test given the following data:
- Sample Size \( n = 56 \)
- Sample Mean \( \bar{x} = 193 \)
- Population Mean \( \mu = 153 \)
- Sample Standard Deviation \( s = 88 \)
- Significance Level \( \alpha = 0.001 \)
To perform this test:
- Calculate the t-score using the formula: \[ t = \frac{\bar{x} - \mu}{s/\sqrt{n}} \]
- Compare the calculated t-score with the critical t-value from the t-distribution table at 55 degrees of freedom (n-1) for a one-tailed test at the 0.001 significance level.
An appropriate conclusion would be drawn based on whether the t-score exceeds the critical t-value.
This evaluation will help determine if there is a statistically significant overestimation of calorie content in the sample population.
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