Intro Stats
4th Edition
ISBN: 9780321826275
Author: Richard D. De Veaux
Publisher: PEARSON
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Textbook Question
Chapter 15, Problem 1E
Website An investment company is planning to upgrade the mobile access to their website, but they’d like to know the proportion of their customers who access it from their smartphones. They draw a random sample of 200 from customers who recently logged in and check their IP address. Suppose that the true proportion of smartphone users is 36%.
- a) What would you expect the shape of the sampling distribution for the sample proportion to be?
- b) What would be the
mean of this sampling distribution? - c) What would be the standard deviation of the sampling distribution?
a.
Expert Solution
To determine
Explain the shape of the sampling distribution for the sample proportion.
Answer to Problem 1E
The shape of the sampling distribution for the sample proportion is unimodal and symmetric.
Explanation of Solution
Given info:
A random sample of 200 is drawn from customers who recently logged in and checked their IP address and the smartphone users true proportion is 36%.
Justification:
Sampling distribution for a proportion:
For all possible samples the distribution of proportion is called the sampling distribution of proportion
- Samples should be independent.
- Sample size should be large.
- The sampling distribution of
Here random sample is drawn by considering 200 investors as a small portion of their customer. Therefore, the sampling distribution for the proportion of 200 investors that use smartphones would be unimodal and symmetrical.
b.
Expert Solution
To determine
Find the mean of this sampling distribution.
Answer to Problem 1E
The mean of this sampling distribution is 0.36.
Explanation of Solution
Justification:
From part (a), the mean for the sampling distribution of proportion is p.
Here, the true proportion smartphone users, is 36% that is, 0.36.
Thus, the mean of this sampling distribution is 0.36.
c.
Expert Solution
To determine
Find the standard deviation of the sampling distribution.
Answer to Problem 1E
The standard deviation of the sampling distribution is 0.034.
Explanation of Solution
Calculation:
From part (a), the standard deviation of
Here proportion p is 0.36 and q is
Substitute p as 0.36, q as 0.64 and n as 200 in the formula,
Thus, the standard deviation of the sampling distribution is 0.034.
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Chapter 15 Solutions
Intro Stats
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