https://file.aiquickdraw.com/mathbot/file/1728792633875ijfnsnfy.jpg

The image you uploaded contains a hypothesis test where all steps seem correct except for the last one, labeled **d.** This is the part about repeating the hypothesis test using the critical value approach.

Let's break down **d**:

1. **Test statistic approach** (which involves calculating the **t-value**):
   - The given test is a one-tailed test (since $ H_a: \mu < 32.48 $).
   - From the image, the critical value is **1.453**. Since this is a one-tailed test, you need to check if your calculated **t-value** is **less than** $-1.453$, not greater than the critical value.

2. **Decision**:
   - You should compare your **t-value** with the critical value.
   - If $ t $-value is **greater than** the negative of the critical value, you cannot reject the null hypothesis. However, if the t-value is smaller than $-1.453$, then you reject $ H_0 $.
   - From the image, it seems that the **t-value** is mistakenly compared in the wrong direction (greater than instead of less than). You need to compare it to $-1.453$ (since it is a left-tailed test).

To correct this:
- The statement should be:
  "The **t** is **less than** the critical value of $-1.453$ (to 3 decimals), so we **do not reject** the null hypothesis."

Would you like further clarification on this? Here are some related questions:

1. How do you calculate the t-value in hypothesis testing?
2. What is the significance of a left-tailed test versus a right-tailed test?
3. Why do we use the critical value approach in hypothesis testing?
4. What are the assumptions behind using a t-test for hypothesis testing?
5. How do you interpret a p-value in the context of this test?

**Tip:** Always check the direction of the hypothesis (one-tailed or two-tailed) to ensure correct comparison of the t-statistic with the critical value!

Develop hypotheses and conduct a hypothesis test to determine whether the mean price of red wine scoring 4.0 or higher on the Vivino Rating System in Providence is less than the population mean of $32.48.

Conduct a one-tailed hypothesis test to determine if the mean price of red wine scoring 4.0 or higher in Providence is less than $32.48. Learn how to set up hypotheses, calculate the t-value, and compare it to the critical value in this university-level statistics problem.

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