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8. Determine the test statistic.     ​(Round to two decimal places as​ needed.)   Determine the​ P-value.   ​(Round to three decimal places as​ needed.)

8. Determine the test statistic.     ​(Round to two decimal places as​ needed.)   Determine the​ P-value.   ​(Round to three decimal places as​ needed.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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8. Determine the test statistic.
 
 
​(Round to two decimal places as​ needed.)
 
Determine the​ P-value.
 
​(Round to three decimal places as​ needed.)
### Crash Test Analysis of Child Booster Seats #### Introduction A safety administration conducted crash tests on child booster seats for cars. The objective was to determine if the booster seats meet the specified safety requirement: the head injury condition (hic) measurement should be less than 1000 hic. #### Data The results from the crash tests, measured in standard head injury condition (hic) units, are as follows: - 732 - 686 - 1122 - 606 - 592 - 480 #### Hypothesis Testing To assess whether the sample comes from a population with a mean less than 1000 hic, we perform statistical hypothesis testing at a 0.05 significance level. **Null Hypothesis (H0):** The mean hic is greater than or equal to 1000. **Alternative Hypothesis (H1):** The mean hic is less than 1000. #### Statistical Analysis To conduct the test, follow these steps: 1. Calculate the sample mean and standard deviation of the given hic values. 2. Use these values to find the test statistic with a t-test for a single sample mean. 3. Determine the P-value associated with the test statistic to evaluate the hypotheses. #### Conclusion Interpret the P-value to determine if it is less than the significance level of 0.05. This will indicate whether we can reject the null hypothesis in favor of the alternative hypothesis. The conclusion will clarify whether the results suggest that all child booster seats meet the specified safety requirement.
Transcribed Image Text:### Crash Test Analysis of Child Booster Seats #### Introduction A safety administration conducted crash tests on child booster seats for cars. The objective was to determine if the booster seats meet the specified safety requirement: the head injury condition (hic) measurement should be less than 1000 hic. #### Data The results from the crash tests, measured in standard head injury condition (hic) units, are as follows: - 732 - 686 - 1122 - 606 - 592 - 480 #### Hypothesis Testing To assess whether the sample comes from a population with a mean less than 1000 hic, we perform statistical hypothesis testing at a 0.05 significance level. **Null Hypothesis (H0):** The mean hic is greater than or equal to 1000. **Alternative Hypothesis (H1):** The mean hic is less than 1000. #### Statistical Analysis To conduct the test, follow these steps: 1. Calculate the sample mean and standard deviation of the given hic values. 2. Use these values to find the test statistic with a t-test for a single sample mean. 3. Determine the P-value associated with the test statistic to evaluate the hypotheses. #### Conclusion Interpret the P-value to determine if it is less than the significance level of 0.05. This will indicate whether we can reject the null hypothesis in favor of the alternative hypothesis. The conclusion will clarify whether the results suggest that all child booster seats meet the specified safety requirement.
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