The question is asking us to develop a 90% confidence interval for the proportion of teens who actually text while driving, based on the survey data provided. This involves several steps:

1. **Identify the sample proportion (p̂):** This is the proportion of teens in the sample who said they text while driving. It is calculated as the number of teens who text while driving divided by the total number of teens surveyed.

$$
\hat{p} = \frac{372}{800}
$$

2. **Determine the standard error (SE) of the sample proportion:** The standard error is calculated using the formula for the standard error of a proportion:

$$
SE = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}
$$

where $ n $ is the sample size (800 in this case).

3. **Find the critical value (z*) for a 90% confidence interval:** For a 90% confidence interval, the critical value (z*) corresponds to the z-score that captures the middle 90% of the standard normal distribution. This value is typically 1.645.

4. **Calculate the margin of error (ME):** The margin of error is found by multiplying the critical value by the standard error:

$$
ME = z^* \times SE
$$

5. **Construct the confidence interval:** The confidence interval is then given by the sample proportion plus and minus the margin of error:

$$
\hat{p} \pm ME
$$

By following these steps, we can develop the 90% confidence interval for the proportion of teens who actually text while driving.

Question

The question is asking us to develop a 90% confidence interval for the proportion of teens who actually text while driving, based on the survey data provided. This involves several steps:

1. **Identify the sample proportion (p̂):** This is the proportion of teens in the sample who said they text while driving. It is calculated as the number of teens who text while driving divided by the total number of teens surveyed.
   
   $$
   \hat{p} = \frac{372}{800}
   $$

2. **Determine the standard error (SE) of the sample proportion:** The standard error is calculated using the formula for the standard error of a proportion:
   
   $$
   SE = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}
   $$
   
   where $ n $ is the sample size (800 in this case).

3. **Find the critical value (z*) for a 90% confidence interval:** For a 90% confidence interval, the critical value (z*) corresponds to the z-score that captures the middle 90% of the standard normal distribution. This value is typically 1.645.

4. **Calculate the margin of error (ME):** The margin of error is found by multiplying the critical value by the standard error:
   
   $$
   ME = z^* \times SE
   $$

5. **Construct the confidence interval:** The confidence interval is then given by the sample proportion plus and minus the margin of error:
   
   $$
   \hat{p} \pm ME
   $$

By following these steps, we can develop the 90% confidence interval for the proportion of teens who actually text while driving.

Knowee AI · Accepted Answer

The question is asking us to develop a 90% confidence interval for the proportion of teens who actually text while driving, based on the survey data provided. This involves several steps:

1. **Identify the sample proportion (p̂):** This is the proportion of teens in the sample who said they text while driving. It is calculated as the number of teens who text while driving divided by the total number of teens surveyed.
   
   $$
   \hat{p} = \frac{372}{800}
   $$

2. **Determine the standard error (SE) of the sample proportion:** The standard error is calculated using the formula for the standard error of a proportion:
   
   $$
   SE = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}
   $$
   
   where $ n $ is the sample size (800 in this case).

3. **Find the critical value (z*) for a 90% confidence interval:** For a 90% confidence interval, the critical value (z*) corresponds to the z-score that captures the middle 90% of the standard normal distribution. This value is typically 1.645.

4. **Calculate the margin of error (ME):** The margin of error is found by multiplying the critical value by the standard error:
   
   $$
   ME = z^* \times SE
   $$

5. **Construct the confidence interval:** The confidence interval is then given by the sample proportion plus and minus the margin of error:
   
   $$
   \hat{p} \pm ME
   $$

By following these steps, we can develop the 90% confidence interval for the proportion of teens who actually text while driving.

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