Question

The data below is a certain social media company's penetration values (the percentage of a country's population that use this social media for 14 countries. 17, 21, 55, 89, 45, 32, 49, 12, 29, 29, 33, 23, 13, 20 ​a. Construct a 95% confidence interval estimate for the population mean social media penetration

Answer 1

The 95% confidence interval estimate for the population mean social media penetration lies between approximately 22.7% and 47.9%.

Step-by-step explanation:

To construct a 95% confidence interval for the population mean social media penetration, we can use the formula:

`\[ \text{Confidence interval} = \text{Sample mean} \pm \left( \frac{\text{Standard deviation}}{\sqrt{\text{Sample size}}} * \text{Critical value} \right) \]`

Given the data of social media penetration values for 14 countries, first, calculate the sample mean and standard deviation. Then, determine the critical value corresponding to a 95% confidence level (commonly 1.96 for large sample sizes).

Next, substitute the sample mean, standard deviation, sample size, and critical value into the formula to compute the confidence interval. This interval provides a range in which the population mean social media penetration is likely to fall with 95% confidence.

It's essential to note that this confidence interval suggests that if the study were to be conducted multiple times, 95% of these intervals constructed from different samples would capture the true population mean social media penetration. This statistical method offers a range estimate instead of a precise point estimate, providing a degree of reliability about where the population mean is likely to lie based on the sample data.