PAJBAK The Asker · Probability and Statistics

An app developer seeks to decide between a green and a blue version of a retail app. The developer releases a beta version of the app, and a user who downloads the app is randomly given the green or the blue version. A week after the download, the average time spent on the retail app by the 105 individuals who downloaded the green version and the 103 individuals who downloaded the blue version were, respectively, 14 minutes (SD = 3.3 minutes) and 11 minutes (SD = 3.1 minutes).

1. What is a 80% confidence interval for the difference between the average time spent by users on the green version of the app and the average time spent by users on the blue version of the app?

2. Consider the following interpretations of this 80% confidence interval, Which of them is correct?

(a) We can be 80% confident that the difference between the average time spent by users on the green and on the blue version of the app, in the population, is within the interval obtained.

(b) We can be 80% confident that the difference between the average time spent by users on the green and on the blue version of the app, in the sample, is within the interval obtained.

(c) There is a .80 probability that the difference between the average time spent by users on the green and on the blue version of the app, in the sample, lies in the interval obtained.

(d) There is a .80 probability that the difference between the average time spent by users on the green and on the blue version of the app, in the population, lies in the interval obtained.

3. The 80% confidence interval included only positive values. Can we be sure that the 99% confidence interval also includes only positive values?

4. What is an implicit assumption that this analysis needs to rely on?

5. Considering the way that this analysis was carried out, which of the following should be said about the population to which the findings can generalize?

(a) The population is all individuals who buy the type of products sold on the retail app.

(b) The population is all individuals with a smartphone.

(c) We should be careful to extend the findings to all potential users of this retail app, because the sample only included individuals who voluntarily downloaded the beta version of the app.

Transcribed Image Text: That if we repeat the same experiment we will obtain the same group averages. That the first users to download the beta version of the app can be regarded as a random sample from the population. That the population averages are equal to the sample averages. That the population of users of the app includes less than 1000 users.
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Transcribed Image Text: That if we repeat the same experiment we will obtain the same group averages. That the first users to download the beta version of the app can be regarded as a random sample from the population. That the population averages are equal to the sample averages. That the population of users of the app includes less than 1000 users.