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Chapter 3: Problem 21

How Many Apps for Your Smartphone? Exercise 3.20 describes a study about smartphone users in the US downloading apps for their smartphone. Of the \(n=355\) smartphone users who had downloaded an app, the average number of apps downloaded was 19.7 (a) Give notation for the parameter of interest, and define the parameter in this context. (b) Give notation for the quantity that gives the best estimate and give its value. (c) What would we have to do to calculate the parameter exactly?

Short Answer

Expert verified
The sought-after parameter of interest is the average number of apps downloaded by all smartphone users in the US (\(\mu\)). The best estimate for it is the sample mean (\(\overline{X}\)) which equals 19.7 based on a survey of 355 users. To calculate \(\mu\) precisely, data from all smartphone users in the U.S. would have to be collected.

Step by step solution

01

Identify the Parameter of Interest

The parameter of interest here is the total average number of apps downloaded by all smartphone users in the U.S, represented as \(\mu\). \(\mu\) is the population mean.
02

Quantify the Best Estimate and Give its Value

The best estimate for the parameter of interest is the sample mean, denoted as \(\overline{X}\). In this case, according to the problem, \(\overline{X}\) is the average number of apps downloaded by the \(n=355\) smartphone users surveyed, which is 19.7.
03

Calculate the Parameter Exactly

To calculate the parameter \(\mu\) exactly, it would be necessary to obtain data from all smartphone users in the US and find the average number of apps they have downloaded. In practice, this is nearly impossible due to the large and constantly changing size of the population.

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