A data set includes times​ (in minutes) of taxi cab rides in New York City yellow cabs during a Friday morning of the same day in a recent year. Using 35 of the times to test the claim that the mean of all such times is less than 15 ​minutes, the accompanying Minitab display is obtained. Test the given claim by using the display provided from Minitab. Use a 0.05 significance level.
LOADING... Click the icon to view the Minitab display.
Question content area bottom
Part 1
Identify the null and alternative hypotheses.
Upper H 0​:
▼
p
mu
sigma
▼
equals
not equals
less than
greater than

enter your response here
Upper H 1​:
▼
sigma
p
mu
▼
not equals
less than
greater than
equals

enter your response here
​(Type integers or decimals. Do not​ round.)

To perform a hypothesis test, we need to identify the null hypothesis \((H_0)\) and the alternative hypothesis \((H_1)\). Given that the problem is testing whether the mean time of the taxi cab rides is **less than** 15 minutes, the hypotheses are stated as follows:

1. **\( H_0 \) (Null Hypothesis)**: The mean time is equal to 15 minutes. This is the default claim we are challenging.
   \[
   H_0: \mu = 15
   \]

2. **\( H_1 \) (Alternative Hypothesis)**: The mean time is less than 15 minutes. This is what we aim to provide evidence for.
   \[
   H_1: \mu < 15
   \]

### Next Steps:
If you have a Minitab display showing the output of a hypothesis test, such as a \( t \)-value, \( p \)-value, and degrees of freedom, we would typically use the \( p \)-value to make a decision based on the significance level of 0.05.

1. If \( p \)-value < 0.05, reject \( H_0 \).
2. If \( p \)-value ≥ 0.05, fail to reject \( H_0 \).

Would you like a detailed interpretation using the Minitab values, or do you have any specific values from the display you'd like me to address?

### Related Questions:
1. What is the critical \( t \)-value for a one-tailed test at the 0.05 significance level with 34 degrees of freedom?
2. How would the conclusion change if the significance level was 0.01?
3. What assumptions are necessary for the \( t \)-test in this scenario to be valid?
4. How do you calculate the \( t \)-statistic manually given sample mean, sample size, and standard deviation?
5. What other hypothesis tests could be used if the sample size or distribution assumptions were different?

**Tip:** In hypothesis testing, always define the null and alternative hypotheses clearly before performing any calculations. This helps maintain clarity and consistency in interpreting the results.

A data set includes times​ (in minutes) of taxi cab rides in New York City yellow cabs during a Friday morning of the same day in a recent year. Using 35 of the times to test the claim that the mean of all such times is less than 15 ​minutes, the accompanying Minitab display is obtained. Test the given claim by using the display provided from Minitab. Use a 0.05 significance level. Identify the null and alternative hypotheses.

Test the claim that the mean time of taxi rides in New York City yellow cabs is less than 15 minutes using a Minitab display. This problem involves hypothesis testing, the t-statistic, and understanding p-values at a 0.05 significance level. Ideal for undergraduate statistics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation