**Study on TV Viewing Hours: Freshmen vs. Seniors**A consultant for a large university conducted a study to compare the number of hours per week that freshmen watch TV versus the number of hours seniors watch. The study's results are presented below. The question is whether there is enough evidence to show that the mean number of hours per week freshmen watch TV is different from the mean number of hours seniors watch, with a significance level of α=0.1.**Data Summary:**| | Freshmen | Seniors ||---|---|---|| n (sample size) | 8 | 4 || x̄ (mean hours) | 18.0 | 11.0 || s (standard deviation) | 7.8740 | 3.9749 |**Hypothesis Testing (Seniors – Freshmen):**1. **Question 1:** What are the critical value(s)? [Space for values] ___ = ___2. **Question 2:** What is the decision? [Space for decision]3. **Question 3:** What is the p-value? Fill in only one of the following statements. - If the Z table is appropriate, p-value = [Space for p-value] - If the t table is appropriate, [Space] < p-value < [Space]This setup assists in hypothesis testing to determine if there is a statistically significant difference between the two groups in terms of TV viewing habits.

Answered: A consultant for a large university…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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**Study on TV Viewing Hours: Freshmen vs. Seniors**

A consultant for a large university conducted a study to compare the number of hours per week that freshmen watch TV versus the number of hours seniors watch. The study's results are presented below. The question is whether there is enough evidence to show that the mean number of hours per week freshmen watch TV is different from the mean number of hours seniors watch, with a significance level of α=0.1.

**Data Summary:**

| | Freshmen | Seniors |
|---|---|---|
| n (sample size) | 8 | 4 |
| x̄ (mean hours) | 18.0 | 11.0 |
| s (standard deviation) | 7.8740 | 3.9749 |

**Hypothesis Testing (Seniors – Freshmen):**

1. **Question 1:**
What are the critical value(s)?
[Space for values] ___ = ___

2. **Question 2:**
What is the decision?
[Space for decision]

3. **Question 3:**
What is the p-value? Fill in only one of the following statements.
- If the Z table is appropriate, p-value = [Space for p-value]
- If the t table is appropriate, [Space] < p-value < [Space]

This setup assists in hypothesis testing to determine if there is a statistically significant difference between the two groups in terms of TV viewing habits.

Expert Solution

Step 1

Let $μ_{1}$ denotes the mean number of hours per week freshmen wash TV, and $μ_{2}$ denotes the mean number of hours per week senior wash TV.

The claim of the test is that the mean number of hours per week freshmen watch TV is different from the mean number of hours per week seniors watch TV. The hypothesis is,

Null hypothesis:

$H_{0} : μ_{1} = μ_{2}$

Alternative hypothesis:

$H_{1} : μ_{1} \neq μ_{2}$

The pooled estimate is,

$\begin{array}{rcl} s_{p}^{2} & = & \frac{(n_{1} - 1) s_{1}^{2} + (n_{2} - 1) s_{2}^{2}}{n_{1} + n_{2} - 2} \\ = & \frac{(8 - 1) 7 . 8740^{2} + (4 - 1) 3 . 9749^{2}}{8 + 4 - 2} \\ = & \frac{481.3986}{10} \\ = & 48.1399 \end{array}$

The test statistic is,

$\begin{array}{rcl} t & = & \frac{{\bar{x}}_{1} - {\bar{x}}_{2}}{\sqrt{s_{p}^{2} (\frac{1}{n_{1}} + \frac{1}{n_{2}})}} \\ = & \frac{18.0 - 11.0}{\sqrt{48.1399 (\frac{1}{8} + \frac{1}{4})}} \\ = & \frac{7}{4.2488} \\ = & 1.6475 \end{array}$

Thus, the test statistic is 1.6475.

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