Assume that Friday morning​ taxi-cab rides have times with a standard deviation of sigmaσequals= 10.1 minutes. A cab driver records times of rides during a Friday afternoon time period and obtains these​ statistics: nequals=16​, x overbarxequals= 18.5 ​minutes, sequals= 12.3 minutes. Use a 0.05 significance level to test the claim that these Friday afternoon times have greater variation than the Friday morning times. Assume that the sample is a simple random sample selected from a normally distributed population.

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Part 1

Let sigmaσ denote the population standard deviation of Friday afternoon​ cab-ride times. Identify the null and alternative hypotheses.

Upper H 0H0​: sigmaσ

▼ 

less than<

not equals≠

equals=

greater than>

enter your response here

Upper H 1H1​: sigmaσ

▼ 

not equals≠

equals=

greater than>

less than<

enter your response here

To test the claim that the Friday afternoon cab-ride times have greater variation than the Friday morning times, we will set up the null and alternative hypotheses.

### Part 1: Hypotheses

1. **Null Hypothesis (H₀)**: The population standard deviation of Friday afternoon cab-ride times is less than or equal to the population standard deviation of Friday morning times.
   - \( H_0: \sigma < 10.1 \)

2. **Alternative Hypothesis (H₁)**: The population standard deviation of Friday afternoon cab-ride times is greater than the population standard deviation of Friday morning times.
   - \( H_1: \sigma > 10.1 \)

### Summary

- \( H_0: \sigma \leq 10.1 \)
- \( H_1: \sigma > 10.1 \)

Would you like to proceed with the test calculations, or do you have any questions? Here are some related questions you might consider:

1. What is the formula for the test statistic in this scenario?
2. How do you interpret the significance level of 0.05 in hypothesis testing?
3. What are the steps to calculate the test statistic and p-value?
4. How do you conclude whether to reject or fail to reject the null hypothesis?
5. What implications would a rejection of the null hypothesis have for the cab company? 

**Tip:** Always check assumptions of normality when conducting hypothesis tests involving variances.

Assume that Friday morning taxi-cab rides have times with a standard deviation of sigmaσequals= 10.1 minutes. A cab driver records times of rides during a Friday afternoon time period and obtains these​ statistics: nequals=16​, x overbarxequals= 18.5 ​minutes, sequals= 12.3 minutes. Use a 0.05 significance level to test the claim that these Friday afternoon times have greater variation than the Friday morning times. Assume that the sample is a simple random sample selected from a normally distributed population. Identify the null and alternative hypotheses.

Explore the hypothesis testing for Friday afternoon taxi-cab ride times, comparing variances with a significance level of 0.05. This problem utilizes statistics with n=16, mean ride time of 18.5 minutes, and a standard deviation of 12.3 minutes against a known variance of 10.1 minutes. Ideal for Grades 11-12 students.

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