The paper "Privacy Policies for Apps Targeted Toward Youth: Descriptive Analysis of Readability describes a
study of the readability of the privacy policies for apps that are targeted toward young people. The reading
grade level (the grade level at which a person would be expected to be able to read and understand the
text without help) was measured for the privacy policies of 30 free apps. The sample mean reading grade
level was reported to be 13.0 (meaning that someone would need to be reading at grade level 13 (first year
of college) to read and understand the policy). The sample standard deviation was 1.3. Suppose that it is
reasonable to regard this sample of 30 free apps as a random sample of free apps targeted toward young
people and that you are interested in learning about the value of 𝜇, the population mean reading grade
level for free apps targeted toward young people.
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To learn about the population mean reading grade level for free apps targeted toward young people, you can use the sample mean and sample standard deviation to construct a confidence interval.
Let's denote 𝜇 as the population mean reading grade level for free apps targeted toward young people.
Since the sample is a random sample, follows certain assumptions (such as normal distribution), and the sample size is reasonably large (n = 30), you can use a t-distribution to construct the confidence interval.
To construct the confidence interval, you need to specify the confidence level. Let's say you want to construct a 95% confidence interval.
The formula for the confidence interval is:
𝑥̄ ± 𝑡 ∗ (s/√n)
where 𝑥̄ is the sample mean reading grade level, t is the t-score corresponding to the desired confidence level and degrees of freedom (df = n - 1), s is the sample standard deviation, and n is the sample size.
Since you don't have the exact t-score, you can use a t-table or statistical software to find the t-score. For a 95% confidence level with 29 degrees of freedom, the t-score is approximately 2.045.
Plugging the values into the formula, the confidence interval becomes:
13.0 ± 2.045 ∗ (1.3/√30)
Simplifying the equation:
13.0 ± 0.445
Therefore, the 95% confidence interval for the population mean reading grade level for free apps targeted toward young people is approximately (12.555, 13.445).
This means we can be 95% confident that the true population mean reading grade level falls within the range of 12.555 and 13.445.
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