1. A software development team is evaluating a new battery-saving feature for their mobile video streaming app. They want to understand how the feature affects the battery drain percentage of a device after one hour of continuous video streaming.
The team initially proposes the following investigative question: "Does the new feature save battery?"
Identify one flaw in this investigative question and state a refined investigative question that addresses the flaw and focuses on a quantitative variable.
To collect initial data, the team posts a link on their official social media page asking followers to download a beta version of the app, stream video for one hour, and report their battery drain percentage.
Identify the sampling method used. Describe a potential source of bias in this sampling method and explain how this bias could affect the estimate of the mean battery drain percentage for all users of the app.
Recognizing the flaw in their initial plan, the team decides to obtain a simple random sample of 50 current app users. The mean battery drain for this sample after one hour of streaming is 12.4 percent, with a standard deviation of 2.1 percent. The distribution of battery drain percentages is approximately symmetric.
One user in the sample reported a battery drain of 18.5 percent. Calculate the z-score for this user's battery drain and interpret it in context. Based on the calculated z-score, is this battery drain considered an outlier? Justify your answer.
In a separate study, the team recruits 120 volunteer app users to participate in an experiment. The volunteers are randomly assigned to either stream video with the battery-saving feature enabled (60 users) or disabled (60 users) for one hour. At the end of the hour, the group with the feature enabled had a significantly lower mean battery drain percentage.
Based on the study design, to what population can the results be generalized? Can the team conclude that the new feature caused the reduction in battery drain? Justify your answers.
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