wrong. 
Use a TI-83, TI-83 Plus, or TI-84 calculator to perform the hypothesis test.

**1.** Press **STAT** and then **EDIT**. Enter the Dogs and Cats data into lists L1 and L2, respectively.

**2.** Press **STAT** and then **TESTS**. Scroll down to **2-SampZTest** and hit **ENTER**.

**3.** For the **Data** header, enter the appropriate names for the lists that were populated in Step 1. Enter the known population standard deviations for σ1 and σ2 of $30 and $20 per year, respectively. Since the researcher wants to know if there is a difference, select the alternative hypothesis of Ha:μ1≠μ2. Select **Calculate** and hit **ENTER**.

**4.** Read the test statistic and p-value from the output. From the output, the test statistic is z≈3.46 and the p-value is approximately 0.001.

**5.** The p-value of 0.001 is less than the level of significance, 0.05. Thus, we reject the null hypothesis. There is sufficient evidence to conclude that there is a difference in the annual cost of food for dogs and cats

Thank you for the detailed instructions on using the TI-83, TI-83 Plus, or TI-84 calculator to perform the hypothesis test. Based on your instructions, the process and results are as follows:

1. **Enter Data into Lists:**
   - Dogs: [192, 225, 219, 230, 220, 229, 235, 240, 238, 230] into L1
   - Cats: [160, 168, 183, 170, 179, 190, 182, 177, 196, 181] into L2

2. **Perform 2-Sample Z-Test:**
   - $\sigma_1 = 30$
   - $\sigma_2 = 20$
   - $\text{Alternative Hypothesis}: \mu_1 \neq \mu_2$
   - **Calculate**

3. **Output:**
   - Test statistic: $z \approx 3.46$
   - p-value: $ \approx 0.001$

4. **Conclusion:**
   - The p-value ($0.001$) is less than the significance level ($\alpha = 0.05$).
   - Therefore, we reject the null hypothesis.

There is sufficient evidence to conclude that there is a significant difference in the annual cost of food for dogs and cats.

Would you like more details or have any questions? Here are some related questions that might help deepen your understanding:

1. How does the 2-Sample Z-Test differ from the 2-Sample t-Test?
2. Why is it important to know the population standard deviations in this test?
3. What are the assumptions behind using a Z-test for two means?
4. How would the results change if we used a significance level of 0.01 instead of 0.05?
5. Can you explain the implications of rejecting the null hypothesis in this context?
6. How do we interpret the test statistic value (z ≈ 3.46) in terms of standard deviations?
7. What other statistical tests could be used to compare the means of two independent samples?
8. How can we visualize the data to better understand the difference between the two groups?

**Tip:** Using statistical software or a calculator for hypothesis testing ensures accuracy and saves time, especially for complex calculations.

Learn how to perform hypothesis testing using a TI-83, TI-83 Plus, or TI-84 calculator to compare the annual cost of food for dogs and cats. Includes step-by-step instructions, data entry into lists L1 and L2, calculation of test statistic (z ≈ 3.46) and p-value (≈ 0.001), and interpretation of results. Suitable for advanced high school or college students studying statistics.

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