#30. Hypothesis Test for a Population Proportion with StatCrunch

TL;DR

A trainer analyzes 36 football injuries and finds that 17 occurred during practices, questioning if the proportion of injuries is less than 0.576.

Transcript

let's do problem number 30 a report by the ncaa states that 57.6 of football injuries occur during practices a head trainer claims that this is too high for his conference so he randomly selects 36 injuries and finds that 17 occurred during practices at the five percent significance level do the data provide sufficient evidence to conclude that the... Read More

Key Insights

• 🏈 Around 57.6% of football injuries occur during practices, according to a report by the NCAA.
• 🏈 The trainer randomly selects and analyzes 36 football injuries.
• ❓ Out of the 36 injuries, 17 were found to have occurred during practices.
• 🏈 The null hypothesis states that the proportion of football injuries is equal to or greater than 0.576.
• 🏈 The alternative hypothesis suggests that the proportion of football injuries is less than 0.576.
• 🤪 The test statistic (Z-stat) is computed to be -1.26.
• ✋ The p-value is calculated to be 0.1038, which is higher than the significance level of 0.05.

Questions & Answers

Q: What is the purpose of the head trainer's analysis?

The trainer aims to determine if the proportion of football injuries during practices is lower than the reported percentage of 57.6%.

Q: How many injuries did the trainer analyze?

The trainer analyzed a total of 36 football injuries.

Q: What is the test statistic obtained from the analysis?

The test statistic (Z-stat) is calculated to be -1.26.

Q: Does the p-value provide sufficient evidence to support the null hypothesis?

No, since the p-value is 0.1038, which is higher than the significance level of 0.05, there is not enough evidence to reject the null hypothesis.

Summary & Key Takeaways

• A head trainer randomly selects 36 football injuries and discovers that 17 of them happened during practices.

• The data revolves around determining if the proportion of football injuries is less than 0.576.

• The trainer uses statistical analysis and hypothesis testing to draw conclusions about the significance of the findings.