A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds. The commercials were for clothes, food, and toys.
 

Clothes	Food	Toys
28	38	53
16	41	44
51	42	48
35	52	56
28	47	63
31	42	53
17	34	48
31	43	58
20	57	47
 	47	51
 	44	51
 	54	 
What is the test statistic? (Round your answer to 4 decimal places.) Take the sample mean, subtract the hypothesized mean, and divide by the standard error of the mean.

To calculate the test statistic for this data set, we need to follow these steps:

### 1. Organize the data
We have the following data for each category (clothes, food, and toys):

- **Clothes**: 28, 16, 51, 35, 28, 31, 17, 31, 20 (9 data points)
- **Food**: 38, 41, 42, 52, 47, 42, 34, 43, 57, 47, 44, 54 (12 data points)
- **Toys**: 53, 44, 48, 56, 63, 53, 48, 58, 47, 51, 51 (11 data points)

### 2. Calculate the sample means for each group
Let’s calculate the sample mean of each category.

### 3. Hypothesized mean
We need to subtract the hypothesized mean from the sample means. You haven’t provided the hypothesized mean, so I’ll assume it’s a value you have or should have from the context of the problem.

### 4. Calculate the standard error of the mean
The standard error of the mean is calculated as:

\[
SE = \frac{s}{\sqrt{n}}
\]

where \( s \) is the standard deviation of the sample and \( n \) is the number of data points.

### 5. Test statistic
The test statistic is given by:

\[
t = \frac{\text{Sample mean} - \text{Hypothesized mean}}{SE}
\]

Let me calculate this step by step using Python for accuracy.Here are the test statistics for each category:

1. **Clothes**:
   - Sample Mean: 28.5556
   - Standard Deviation: 10.7367
   - Standard Error: 3.5789
   - Test Statistic: \(-3.1977\)

2. **Food**:
   - Sample Mean: 45.0833
   - Standard Deviation: 6.6805
   - Standard Error: 1.9285
   - Test Statistic: \(2.6359\)

3. **Toys**:
   - Sample Mean: 52.0000
   - Standard Deviation: 5.4589
   - Standard Error: 1.6459
   - Test Statistic: \(7.2907\)

These test statistics compare each sample mean to the hypothesized mean of 40 (which was assumed).

Would you like more details or clarification on any part? Here are five related questions to further explore:

1. How do you interpret the negative test statistic for the clothes data?
2. What does the large test statistic for the toys data suggest?
3. How does changing the hypothesized mean affect the test statistic?
4. Can you apply a different confidence level to these results?
5. What are the implications of the standard error for each group?

**Tip**: Always check the degrees of freedom when using a t-test for small sample sizes, as it affects the critical values for the test statistic.

A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds. The commercials were for clothes, food, and toys.

Clothes	Food	Toys
28	38	53
16	41	44
51	42	48
35	52	56
28	47	63
31	42	53
17	34	48
31	43	58
20	57	47
 	47	51
 	44	51
 	54

What is the test statistic? (Round your answer to 4 decimal places.) Take the sample mean, subtract the hypothesized mean, and divide by the standard error of the mean.

Explore a hypothesis test examining the effect of TV commercials (clothes, food, and toys) on the attention span of 12-year-old children. Learn how to calculate the test statistic using sample means, standard errors, and a t-test. Suitable for high school students in Grades 10-12.

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