Intro Stats, Books a la Carte Edition (5th Edition)
Intro Stats, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780134210285
Author: Richard D. De Veaux, Paul Velleman, David E. Bock
Publisher: PEARSON
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Chapter 13, 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%.

  1. a) What would you expect the shape of the sampling distribution for the sample proportion to be?
  2. b) What would be the mean of this sampling distribution?
  3. c) What would be the standard deviation of the sampling distribution?

a.

Expert Solution
Check Mark
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 p^ is formed by normal model with mean p and standard deviation of p^ is, SD(p^)=pqn where q=1p.

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
Check Mark
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
Check Mark
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 p^ is, SD(p^)=pqn.

Here proportion p is 0.36 and q is 0.64=(10.36) and total sample is 200.

Substitute p as 0.36, q as 0.64 and n as 200 in the formula,

SD(p^)=0.36(0.64)200=0.2304200=0.0011520.034

Thus, the standard deviation of the sampling distribution is 0.034.

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Chapter 13 Solutions

Intro Stats, Books a la Carte Edition (5th Edition)

Ch. 13.5 - Prob. 11JCCh. 13 - Website An investment company is planning to...Ch. 13 - Marketing The proportion of adult women in the...Ch. 13 - Prob. 3ECh. 13 - Character recognition An automatic character...Ch. 13 - Prob. 5ECh. 13 - Hows life? Gallup regularly conducts a poll using...Ch. 13 - Prob. 7ECh. 13 - Prob. 8ECh. 13 - Send more money The philanthropic organization in...Ch. 13 - Character recognition, again The automatic...Ch. 13 - Prob. 11ECh. 13 - Prob. 12ECh. 13 - Prob. 13ECh. 13 - Spanking In a 2015 Pew Research study on trends in...Ch. 13 - Prob. 15ECh. 13 - Smoking The Gallup poll described in Exercise 6...Ch. 13 - Prob. 17ECh. 13 - Prob. 18ECh. 13 - Graduation Its believed that as many as 25% of...Ch. 13 - Hiring In preparing a report on the economy, we...Ch. 13 - Margin of error A TV newscaster reports the...Ch. 13 - Another margin of error A medical researcher...Ch. 13 - Conditions For each situation described below,...Ch. 13 - More conditions Consider each situation described....Ch. 13 - Conclusions A catalog sales company promises to...Ch. 13 - More conclusions In January 2002, two students...Ch. 13 - Confidence intervals Several factors are involved...Ch. 13 - Confidence intervals, again Several factors are...Ch. 13 - Cars What fraction of cars made in Japan? The...Ch. 13 - Prob. 30ECh. 13 - Mislabeled seafood In 2013 the environmental group...Ch. 13 - Mislabeled seafood, second course A Consumer...Ch. 13 - Prob. 33ECh. 13 - Prob. 34ECh. 13 - Prob. 35ECh. 13 - Take the offer First USA, a major credit card...Ch. 13 - Teenage drivers An insurance company checks police...Ch. 13 - Junk mail Direct mail advertisers send...Ch. 13 - Prob. 39ECh. 13 - Prob. 40ECh. 13 - Prob. 41ECh. 13 - Gambling A city ballot includes a local initiative...Ch. 13 - Rickets Vitamin D, whether ingested as a dietary...Ch. 13 - Teachers A 2011 Gallup poll found that 76% of...Ch. 13 - Prob. 45ECh. 13 - Back to campus ACT, Inc. reported that 74% of 1644...Ch. 13 - Deer ticks Wildlife biologists inspect 153 deer...Ch. 13 - Prob. 48ECh. 13 - Graduation, again As in Exercise 19, we hope to...Ch. 13 - Better hiring info Editors of the business report...Ch. 13 - Prob. 51ECh. 13 - Another pilot study During routine screening, a...Ch. 13 - Prob. 53ECh. 13 - Amendment A TV news reporter says that a proposed...
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