**Hypothesis Testing Example: Miniature Golf Scores**A large group of friends went miniature golfing together at a golf course and decided to play on two teams. A random sample of scores from each of the two teams is shown below.At $ \alpha = 0.05 $, is there enough evidence to conclude there is a difference in mean scores between the two teams?| | ||-------|-------|| **Team 1** | 61, 44, 52, 47, 56, 63, 62, 55 || **Team 2** | 56, 40, 42, 58, 48, 52, 51 |---**a) Based on reading the problem, how do we know we are working with a hypotheses test ($ H_0 $ and $ H_1 $)? This question has two possible answers.**- [ ] Asks us to find (estimate) the % confidence interval of the population (true) mean.- [ ] Asks us to find the sample size (how many or how large).- [x] $ \alpha $ is provided.- [ ] Asks us to find (estimate) the % confidence interval of the population (true) proportion.- [x] Asks if there is evidence or can we conclude something.---**Hypotheses**- $ H_0: \mu_1 - \mu_2 = 0 $ (Not the claim)- $ H_1: \mu_1 - \mu_2 \neq 0 $ (Claim)---These questions and setup are designed to guide students through understanding hypothesis testing by identifying key information, such as the significance level $ \alpha $ and whether the problem is asking for comparative conclusions based on statistical evidence. ## Educational Website Content### Critical Values and Test Formulas**Select the Critical Values (CV):**- **CV1 =** [Select an answer] $ \left( \_\_\_ , \_\_\_ \right) $- **CV2 =** [Select an answer] $ \left( \_\_\_ , \_\_\_ \right) $### Round to Two Decimal Places:- **CV1 =** [Input Box]- **CV2 =** [Input Box]---### Test Value Formula Selection:**f) What formula will we use for the test value?**1. $ z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}} $2. $ z = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} $3. $ z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\hat{p} \cdot \hat{q} \cdot \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}} $4. $ t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} $5. $ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} $### DescriptionThis section guides you on how to select and calculate critical values and test value formulas. The formulas presented include both $ z $-scores and $ t $-scores for hypothesis testing under various conditions, such as comparing population proportions or means.

Name: **Hypothesis Testing Example: Miniature Golf Scores**A large group of
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Description: **Hypothesis Testing Example: Miniature Golf Scores**A large group of friends went miniature golfing together at a golf course and decided to play on two teams. A random sample of scores from each of the two teams is shown below.At \( \alpha = 0.05

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CV, = Select an answer v CV2 = Select an answer v %3D Round to Two Decimal Places CV, = CV2 = f) What formula will we use for the test value? p – p Oz = V (71 – F2) – (µ1 – H2) Ot = n1 (P1 – P2) – (Pi – p2) Oz = | n1 n2 Ot = Oz =

CV, = Select an answer v CV2 = Select an answer v %3D Round to Two Decimal Places CV, = CV2 = f) What formula will we use for the test value? p – p Oz = V (71 – F2) – (µ1 – H2) Ot = n1 (P1 – P2) – (Pi – p2) Oz = | n1 n2 Ot = Oz =

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Question

**Hypothesis Testing Example: Miniature Golf Scores**

A large group of friends went miniature golfing together at a golf course and decided to play on two teams. A random sample of scores from each of the two teams is shown below.

At $ \alpha = 0.05 $, is there enough evidence to conclude there is a difference in mean scores between the two teams?

| | |
|-------|-------|
| **Team 1** | 61, 44, 52, 47, 56, 63, 62, 55 |
| **Team 2** | 56, 40, 42, 58, 48, 52, 51 |

---

**a) Based on reading the problem, how do we know we are working with a hypotheses test ($ H_0 $ and $ H_1 $)? This question has two possible answers.**

- [ ] Asks us to find (estimate) the % confidence interval of the population (true) mean.
- [ ] Asks us to find the sample size (how many or how large).
- [x] $ \alpha $ is provided.
- [ ] Asks us to find (estimate) the % confidence interval of the population (true) proportion.
- [x] Asks if there is evidence or can we conclude something.

---

**Hypotheses**

- $ H_0: \mu_1 - \mu_2 = 0 $ (Not the claim)
- $ H_1: \mu_1 - \mu_2 \neq 0 $ (Claim)

---

These questions and setup are designed to guide students through understanding hypothesis testing by identifying key information, such as the significance level $ \alpha $ and whether the problem is asking for comparative conclusions based on statistical evidence.

## Educational Website Content

### Critical Values and Test Formulas

**Select the Critical Values (CV):**

- **CV1 =** [Select an answer] $ \left( \_\_\_ , \_\_\_ \right) $
- **CV2 =** [Select an answer] $ \left( \_\_\_ , \_\_\_ \right) $

### Round to Two Decimal Places:

- **CV1 =** [Input Box]
- **CV2 =** [Input Box]

---

### Test Value Formula Selection:

**f) What formula will we use for the test value?**

1. $ z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}} $

2. $ z = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} $

3. $ z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\hat{p} \cdot \hat{q} \cdot \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}} $

4. $ t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} $

5. $ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} $

### Description

This section guides you on how to select and calculate critical values and test value formulas. The formulas presented include both $ z $-scores and $ t $-scores for hypothesis testing under various conditions, such as comparing population proportions or means.

Expert Solution

Step 1:- CV1 calculation

Step 2:- CV2

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