https://file.aiquickdraw.com/mathbot/file/1729969607575eb5v40s7.jpg

This question is asking for a hypothesis test to determine if the mean price of a cup of coffee is different from $3.99 at a 10% significance level. Here’s how to approach each part of the question:

### a) Hypotheses

1. **Null Hypothesis ($ H_0 $)**: The mean price of a cup of coffee is equal to $3.99.
   - $ H_0: \mu = 3.99 $

2. **Alternative Hypothesis ($ H_1 $)**: The mean price of a cup of coffee is not equal to $3.99.
   - $ H_1: \mu \neq 3.99 $

### b) Decision Based on p-value

The p-value provided is 0.2531. Since the significance level ($ \alpha $) is 0.10, we can compare the p-value to $ \alpha $:

- **If p-value $ \leq \alpha $**: Reject $ H_0 $.
- **If p-value $ > \alpha $**: Fail to reject $ H_0 $.

In this case, the p-value (0.2531) is greater than $ \alpha $ (0.10), so we **fail to reject the null hypothesis**.

### Summary Statement

Since we fail to reject the null hypothesis, the correct summary would be:
- "There is not enough evidence to conclude that the population mean price of a cup of coffee is not equal to $3.99."

---

Let me know if you’d like further details or have any questions!

### Further Questions:
1. How do we calculate the p-value in a hypothesis test?
2. What does it mean when we fail to reject the null hypothesis?
3. How can we determine if a hypothesis test is one-tailed or two-tailed?
4. What are the steps to conduct a hypothesis test for the population mean?
5. How does changing the significance level affect our decision?

### Tip:
Always check if your hypothesis test is one-tailed or two-tailed, as this affects the interpretation of p-values and critical values.

The mean price of a cup of coffee in Portland, OR is $3.99. The owner of a new coffee house believes that the mean price of coffee is different in their neighborhood. A sample of 8 coffee prices from other local coffee shops in their area are shown below. Test the claim that the mean price of a cup of coffee is not equal to $3.99 using a 10% level of significance. Assume that the coffee prices are normally distributed.

Perform a hypothesis test to determine if the mean coffee price is different from $3.99, using a 10% significance level. This example includes sample data, null and alternative hypothesis, p-value interpretation, and hypothesis testing steps. 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