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The image contains five hypothesis testing problems where you're asked to set up the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_a\)) for each scenario. Below is a detailed solution:

### 1. Online Retailer - More Than 90% of Visitors Make a Purchase
- **\(H_0\)**: The proportion of visitors who make a purchase is less than or equal to 90%.
  \[
  H_0: p \leq 0.90
  \]
- **\(H_a\)**: The proportion of visitors who make a purchase is greater than 90%.
  \[
  H_a: p > 0.90
  \]

### 2. Soda Machine - Dispenses 500 Milliliters Per Bottle
- **\(H_0\)**: The mean amount of soda dispensed is 500 milliliters.
  \[
  H_0: \mu = 500 \text{ mL}
  \]
- **\(H_a\)**: The mean amount of soda dispensed is not 500 milliliters.
  \[
  H_a: \mu \neq 500 \text{ mL}
  \]

### 3. Coffee Advertisement - Amount of Pure Milk in a Cup of Coffee
- **\(H_0\)**: The mean amount of pure milk in a cup of coffee is 0.1 liters.
  \[
  H_0: \mu = 0.1 \text{ L}
  \]
- **\(H_a\)**: The mean amount of pure milk in a cup of coffee is not 0.1 liters.
  \[
  H_a: \mu \neq 0.1 \text{ L}
  \]

### 4. Marketers - At Least 85% of Adults Own a Cell Phone
- **\(H_0\)**: The proportion of adults who own a cell phone is less than 85%.
  \[
  H_0: p < 0.85
  \]
- **\(H_a\)**: The proportion of adults who own a cell phone is at least 85%.
  \[
  H_a: p \geq 0.85
  \]

### 5. Researcher - Students Spend an Average of 23 Hours Preparing for Final Exams
- **\(H_0\)**: The mean time spent preparing for final exams is 23 hours.
  \[
  H_0: \mu = 23 \text{ hours}
  \]
- **\(H_a\)**: The mean time spent preparing for final exams is not 23 hours.
  \[
  H_a: \mu \neq 23 \text{ hours}
  \]

---

Would you like more details on any of these setups or have any other questions?

Here are 5 questions you might consider based on the content:

1. How do you determine whether to use a one-tailed or two-tailed test in hypothesis testing?
2. What is the significance level in hypothesis testing, and how is it chosen?
3. Can you explain Type I and Type II errors in the context of hypothesis testing?
4. How do you calculate the test statistic for a proportion test?
5. What are the steps involved in performing a hypothesis test from start to finish?

**Tip:** Always clearly define your null and alternative hypotheses before conducting any statistical test to ensure the correct interpretation of results.

Set up the null hypothesis and the alternative hypothesis using the symbolic form for the following problems:

1. An online retailer believes that more than 90% of the visitors to its website will make a purchase.
2. A soda machine is set to dispense 500 milliliters per bottle. A sample of 40 bottles is selected at random to determine whether the machine is overfilling bottles.
3. A cafe advertises that it puts 0.1 liter of pure milk in a cup of coffee. A customer group thinks the coffee contains less than 0.1 liter of pure milk and wishes to test this. To perform the test, the customer group selects a random sample of 30 cups of coffee to test the milk's claim.
4. Marketers believe that at least 85% of adults own a cell phone.
5. A researcher believes that students in a 4-year college spend an average of 23 hours preparing for 5 final exams each semester with a standard deviation of 7.3 hours.

Learn how to set up null and alternative hypotheses for various real-world scenarios involving proportions and means. This exercise covers key statistical concepts such as hypothesis testing, proportions, and means, suitable for undergraduate statistics students.

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