**Report the critical value for the following hypothesis test question?**

**For a two tale test and right tale test report the positive value.**

**For a left tale test report the negative value.**

A student advisor is interested to see if students finish their studies in more than 4 years. A sample **of 40** students is taken. **18 of them** have finished studies in more than 4 years. 

We want to be 90% certain.

Answer:



The scenario you've presented involves testing whether students finish their studies in more than 4 years. Here's how we would calculate the critical values for different tests based on the information provided:

### Given Information:
- **Sample size (n):** 40
- **Number of students finishing in more than 4 years (x):** 18
- **Significance level (α):** 10% or 0.10 (since we want to be 90% certain)

### Step 1: Determine the Type of Test
The problem asks for different critical values depending on the type of test:
- **Two-tailed test**: Tests for whether students finish their studies in a time significantly different from 4 years (both more and less than 4 years).
- **Right-tailed test**: Tests for whether students finish in more than 4 years (which is the direction suggested by the problem).
- **Left-tailed test**: Tests for whether students finish in less than 4 years.

### Step 2: Identify the Z-critical values
For a significance level of 10% (α = 0.10), the critical value depends on the type of test:

- **Two-tailed test**: This splits α into two tails, so each tail has 5% (0.05). 
    - The critical Z-value for a two-tailed test at 90% confidence is ±1.645.
  
- **Right-tailed test**: Here, the entire α (10%) is in the right tail.
    - The critical Z-value for a right-tailed test at 90% confidence is **1.28**.

- **Left-tailed test**: Here, the entire α (10%) is in the left tail.
    - The critical Z-value for a left-tailed test at 90% confidence is **-1.28**.

### Critical Values Summary:
- **Two-tailed test**: Z = ±1.645
- **Right-tailed test**: Z = **1.28**
- **Left-tailed test**: Z = **-1.28**

These Z-values are the critical values based on the standard normal distribution for the specified tests.

Let me know if you want more details or have questions! Here are some related questions for deeper understanding:

1. How do we calculate the p-value for a hypothesis test?
2. What is the difference between a one-tailed and a two-tailed test?
3. How does the sample size affect the critical value in hypothesis testing?
4. Why do we use a 90% confidence level, and what would change if we used 95%?
5. What role does the standard error play in hypothesis testing?

**Tip**: Always check whether your test should be one-tailed or two-tailed based on the research question—it determines how you split the significance level (α).

Report the critical value for the following hypothesis test question? For a two-tailed test and right-tailed test report the positive value. For a left-tailed test report the negative value. A student advisor is interested to see if students finish their studies in more than 4 years. A sample of 40 students is taken. 18 of them have finished studies in more than 4 years. We want to be 90% certain.

This page provides a detailed solution to calculate the critical values for a hypothesis test where a student advisor wants to determine if students finish their studies in more than 4 years. The sample includes 40 students, 18 of whom finished in more than 4 years. We use Z-scores for 90% confidence to find critical values for two-tailed, right-tailed, and left-tailed tests.

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