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A Pew Research study regarding cell phones asked questions about cell phone experience. One growing concern is unsolicited advertising in the form of text messages. Pew asked 1150 cell phone owners, "Have you ever received unsolicited text messages on your cell phone from advertisers?" and 17% reported that they had. a) State the parameter you want to estimate. b) Check conditions and identify the appropriate inference method. c) If the conditions have been met, perform the calculations for a 95% confidence interval. If conditions have not been met, state the condition that has been violated. d) If you were able to complete c), interpret your interval in the context of the problem. 2. The 2013 International Bedroom Poll surveyed about 250 randomly sampled adult residents in each of six countries asking about their sleep habits. Sleep researchers generally report that people who regularly use their computers or laptops in the hour before trying to go to sleep are less likely to report getting a good night's sleep, more likely to be categorized as "sleepy," and more likely to drive drowsy than their counterparts. The poll found that 128, or 51%, of 251 U.S. respondents reported using a computer, laptop, or electronic tablet in the hour before trying to go to sleep almost every night. By contrast, 162, or 65%, of 250 Japanese respondents made the same admission. What does a confidence interval say about the difference in sleep habits? a) State the parameter you want to estimate. b) Check conditions and identify the appropriate inference method. c) If the conditions have been met, perform the calculations for a 95% confidence interval for the difference in proportions. If conditions have not been met, state the condition that has been violated. d) If you were able to complete c), interpret your interval in the context of the problem. 3. In a March 2016 survey by Gallup of 1019 U.S. adults, 65% believe that global warming is due more to human activity than natural changes in the environment. The poll reports a margin of error of 4%. Suppose an environmental group planning a follow-up survey of voters' opinions on global warming wants to determine a 95% confidence interval with a margin of error of no more than +2%. How large a sample does the group need?

Name: 1 a pew research study regarding cell phones asked questions about cell phone experience one growing concern is unsolicited advertising in the form of text messages pew asked 1150 cell phone 88505
Uploaded: 2024-01-10T21:18:09-08:00
Duration: 8 min 58 s
Channel: Ana Carolina Da Cruz
Description: 1 a pew research study regarding cell phones asked questions about cell phone experience one growing concern is unsolicited advertising in the form of text messages pew asked 1150 cell phone 88505

2. The 2013 International Bedroom Poll surveyed about 250 randomly sampled adult residents in each of six countries asking about their sleep habits. Sleep researchers generally report that people who regularly use their computers or laptops in the hour before trying to go to sleep are less likely to report getting a good night's sleep, more likely to be categorized as "sleepy," and more likely to drive drowsy than their counterparts. The poll found that 128, or 51%, of 251 U.S. respondents reported using a computer, laptop, or electronic tablet in the hour before trying to go to sleep almost every night. By contrast, 162, or 65%, of 250 Japanese respondents made the same admission. What does a confidence interval say about the difference in sleep habits?
a) State the parameter you want to estimate.
b) Check conditions and identify the appropriate inference method.
c) If the conditions have been met, perform the calculations for a 95% confidence interval for the difference in proportions. If conditions have not been met, state the condition that has been violated.
d) If you were able to complete c), interpret your interval in the context of the problem.

3. In a March 2016 survey by Gallup of 1019 U.S. adults, 65% believe that global warming is due more to human activity than natural changes in the environment. The poll reports a margin of error of 4%. Suppose an environmental group planning a follow-up survey of voters' opinions on global warming wants to determine a 95% confidence interval with a margin of error of no more than +2%. How large a sample does the group need?

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Ana Carolina Da Cruz

01/10/2024

Step 1

a) The parameter we want to estimate is the population proportion (p) of cell phone owners who have received unsolicited text messages from advertisers. b) Conditions: - Random sample: Assuming the 1150 cell phone owners were randomly selected. - Show more…

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A Pew Research study regarding cell phones asked questions about cell phone experience. One growing concern is unsolicited advertising in the form of text messages. Pew asked 1150 cell phone owners, "Have you ever received unsolicited text messages on your cell phone from advertisers?" and 17% reported that they had. a) State the parameter you want to estimate. b) Check conditions and identify the appropriate inference method. c) If the conditions have been met, perform the calculations for a 95% confidence interval. If conditions have not been met, state the condition that has been violated. d) If you were able to complete c), interpret your interval in the context of the problem. 2. The 2013 International Bedroom Poll surveyed about 250 randomly sampled adult residents in each of six countries asking about their sleep habits. Sleep researchers generally report that people who regularly use their computers or laptops in the hour before trying to go to sleep are less likely to report getting a good night's sleep, more likely to be categorized as "sleepy," and more likely to drive drowsy than their counterparts. The poll found that 128, or 51%, of 251 U.S. respondents reported using a computer, laptop, or electronic tablet in the hour before trying to go to sleep almost every night. By contrast, 162, or 65%, of 250 Japanese respondents made the same admission. What does a confidence interval say about the difference in sleep habits? a) State the parameter you want to estimate. b) Check conditions and identify the appropriate inference method. c) If the conditions have been met, perform the calculations for a 95% confidence interval for the difference in proportions. If conditions have not been met, state the condition that has been violated. d) If you were able to complete c), interpret your interval in the context of the problem. 3. In a March 2016 survey by Gallup of 1019 U.S. adults, 65% believe that global warming is due more to human activity than natural changes in the environment. The poll reports a margin of error of 4%. Suppose an environmental group planning a follow-up survey of voters' opinions on global warming wants to determine a 95% confidence interval with a margin of error of no more than +2%. How large a sample does the group need?

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Transcript

00:01 So for the first part of this question, we are interested in the proportion of people that receive unsolicited text messages on their cell phone from advert.

00:14 In this case, people that they don't want to, right? so that's the parameter we are interested in.

00:20 So we're going to say here that we are interested in the proportion of people that receive that kind of message on their cell phone.

00:31 So the conditions here for computing the confidence interval for a proportion is given by two quantities, aside from the fact that we should have a random sample.

00:44 So we should select those people to participate in this study at random.

00:51 So the conditions that we need to check is that the expected number of people that are are receiving that kind of text messages, it should be greater than 5, and those people that don't receive this also should be greater than 5.

01:07 So this is given by the number of people in the sample times the proportion that we have, and for the other one is the number of people times 1 minus the proportion.

01:18 So for both of them, we have this to be greater or equal than 5, which is true for this question so we can always double check that so if you multiply in this case 1 ,150 by 0 ,17 this is greater than 5 and if you multiply this by 1 minus 0 ,17 which is 0 ,83 this is also greater than 5 and i'm assuming that we have a random example.

01:49 So because we have here in this case we want to find the confidence interval, the appropriate inference method for this case is a proportion confidence interval here or confidence interval for a proportion and because we want to estimate that parameter.

02:13 So that's why in the we are computing this.

02:16 So for the 95 % confidence interval, the critical values in this table is 196, which means that the formula here that we're going to use is the value of the proportion in the sample, which is given by the 17%, the reported that they had received, those kind of text messages.

02:36 So we write the proportion instead of the percentage.

02:39 Then we'll plus and minus the the critical value coming from the polynomial distribution, and multiply this by the square root of the proportion that they found times 1 minus the same value divided by the sample size.

02:55 So by considering this plus and minus, we are going to get two values.

02:59 So we are going to estimate here with a specific amount of confidence, which is this 95%, that the proportion is between these two values.

03:08 This so that will be the answer for this item which is this is a letter c instead of d let me just check here b s a b c okay so i'm gonna consider that this is a support of b and then c for d we need to make the interpretation so the interpretation here considers this saying how confident we are that the proportion is inside the confidence interval.

03:49 So what we write is that we are 95 % confident that the true proportion is within the confidence interval that we computed in item c.

03:59 So now for the second question will be something similar where we are comparing two populations.

04:05 So the parameter of interest here will be the difference between the proportion between the two populations.

04:13 So what we're gonna write is the parameter is the difference between the proportion of people in the us versus the proportion of people in japan that uses a computer, laptop, electronic device, for example tablet, in the hour before trying to go to sleep almost every night.

04:33 So that's the parameter that we are interested in.

04:35 So it is the difference between these two proportions...

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