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 34 apps that were available for purchase. The
sample mean reading grade level was reported to be 12.5 (meaning that someone would need to be
reading at grade level 12.5 (senior in high school) to read and understand the policy). The sample standard
deviation was 1.8. Suppose that it is reasonable to regard this sample of 34 apps that are available for
purchase as a random sample of apps available for purchase that are targeted toward young people and
that you are interested in learning about the value of 𝜇, the population mean reading grade level for apps
available for purchase that are targeted toward young people
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The parameter of interest in this study is the population mean reading grade level (𝜇) for apps available for purchase that are targeted toward young people.
Based on the sample of 34 apps, the sample mean reading grade level was reported to be 12.5, and the sample standard deviation was 1.8.
To learn about the value of 𝜇, we can use statistical inference techniques. One common approach is to construct a confidence interval for 𝜇. With the sample mean and standard deviation, we can calculate the standard error of the mean (SE). Assuming the sample follows a normal distribution, we can use the t-distribution to construct the confidence interval.
The formula to calculate the standard error is:
SE = s / √n
Where s is the sample standard deviation and n is the sample size.
Assuming a desired confidence level (such as 95%), we can find the appropriate t-value from the t-distribution table. Let's say for a sample size of 34, the critical t-value for a 95% confidence level is 2.032.
The formula to calculate the confidence interval is:
Confidence Interval = sample mean ± (t-value * SE)
Substituting the values, we get:
Confidence Interval = 12.5 ± (2.032 * 1.8 / √34)
By calculating the above expression, we can obtain the confidence interval within which we can estimate the population mean reading grade level for apps available for purchase that are targeted toward young people.
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