Question

In: Statistics and Probability

1. A study conducted in March 2009 found that about half of U.S. adults trusted the...

1. A study conducted in March 2009 found that about half of U.S. adults trusted the U.S. government more than U.S. business to solve the economic problems of the United States. However, when the population is subdivided by political party affiliation, the results are very different. The study showed that 72% of Democrats trusted the government more, but only 29% of Republicans trusted the government more. Suppose that you are in charge of updating the study. You will take a national sample of Democrats and a national sample of Republicans and then try to use the results to show statistical evidence that the proportion of Democrats trusting the government more than business is greater than the proportion of Republicans trusting the government more tan business.

a. What are the null and alternative hypotheses? b.

What is a Type I error in the context of this study?

c. What is a Type II error in the context of this study?

Solutions

Expert Solution

a. The hypothesis is,

Null hypothesis is that the proportion of Democrats trusting the government more than business is equal to the proportion of Republicans trusting the government more than business.

Alternate Hypothesis is that the proportion of Democrats trusting the government more than business is greater than the proportion of Republicans trusting the government more than business.

b.

Type I error occurs when we reject the true null hypothesis.

If we reject that the the proportion of Democrats trusting the government more than business is equal to the proportion of Republicans trusting the government more than business. When in fact they are equal, then we commit type I error.

c.

Type II occurs when we fail to reject the false null hypothesis.

If we fail to reject that the the proportion of Democrats trusting the government more than business is equal to the proportion of Republicans trusting the government more than business. When in fact they are unequal(i.e., the proportion of Democrats is greater than the proportion of Republicans, then we commit type II error.

orchestra answered 1 year ago
Next > < Previous

Related Solutions

IAB conducted a study of U.S. online adults that included 416 tablet owners. The study found...
IAB conducted a study of U.S. online adults that included 416 tablet owners. The study found that 221 tablet owners use their tablet while watching TV, TV Experience - Attitudes and Usage across Multiple Screens - The authors of the report imply that the survey proves that more than half of all tablet owners use their tablet while watching TV at least once per day. Use the five-step p-value approach to hypothesis testing and a 0.05 level of significance to...
A university conducted a study of online adults that included 419 tablet owners. The study found...
A university conducted a study of online adults that included 419 tablet owners. The study found that 215 tablet owners use their tablet while watching TV. The authors of the report imply that the survey proves that more than half of all tablet owners use their tablet while watching TV at least once per day. Complete parts (a) through (d) below. Complete the five-step p-value approach to hypothesis testing and a 0.05 level of significance to try to prove that...
A university conducted a study of online adults that included 419 tablet owners. The study found...
A university conducted a study of online adults that included 419 tablet owners. The study found that 215 tablet owners use their tablet while watching TV. The authors of the report imply that the survey proves that more than half of all tablet owners use their tablet while watching TV at least once per day. Complete parts (a) through (d) below. a. Use the five-step p-value approach to hypothesis testing and a 0.05 level of significance to try to prove...
A university conducted a study of online adults that included 419 tablet owners. The study found...
A university conducted a study of online adults that included 419 tablet owners. The study found that 215 tablet owners use their tablet while watching TV. The authors of the report imply that the survey proves that more than half of all tablet owners use their tablet while watching TV at least once per day. Complete parts (a) through (d) below. a. Use the five-step p-value approach to hypothesis testing and a 0.05 level of significance to try to prove...
A university conducted a study of online adults that included 405405 tablet owners. The study found...
A university conducted a study of online adults that included 405405 tablet owners. The study found that 213213 tablet owners use their tablet while watching TV. The authors of the report imply that the survey proves that more than half of all tablet owners use their tablet while watching TV at least once per day. Complete parts​(a) through​ (d) below. a. Use the​ five-step p-value approach to hypothesis testing and a 0.050.05 level of significance to try to prove that...
The Pew Research Center recently conducted a survey of 1007 U.S. adults and found that 85%...
The Pew Research Center recently conducted a survey of 1007 U.S. adults and found that 85% of those surveyed know what Twitter is. Using the survey results construct a 95% confidence interval estimate of the percentage of all adults who know what Twitter is. Round the percentages to the first decimal place. (c) Explain why it would or would not be okay for a newspaper to make this statement: “Based on results from a recent survey, more than 3 out...
3. The Pew Research Center conducted a survey in 2019 asking U.S. adults about their experiences...
3. The Pew Research Center conducted a survey in 2019 asking U.S. adults about their experiences dating online. In a random sample of 200 adults aged 18-49, 114 said dating sites are a safe way to meet people. In a random sample of 200 adults aged 50+, 82 said dating sites are a safe way to meet people. Research question: Are U.S. adults aged 18-49 more likely to say dating sites are safe than those aged 50+? a. What are...
4. The Pew Research Center conducted a survey in 2019 asking U.S. adults about their experiences...
4. The Pew Research Center conducted a survey in 2019 asking U.S. adults about their experiences dating online. In a random sample of 100 adults who had dated online, 25 said dating sites made them feel insecure. Research question: Is the amount of online daters who believe dating sites make them feel insecure different than a third? a. Compute the value of the statistic. b. What are the hypothesis statements to answer the research question? c. Are the appropriate conditions...
A study published in 2009 (Goldstein et al, 2009) asked a random selection of 499 adults...
A study published in 2009 (Goldstein et al, 2009) asked a random selection of 499 adults from various regions in Israel to complete a survey about whether or not they read while using the toilet. The researchers conducted a test of Ho: pi = 0.5 versus Ha: pi ≠ 0.5 where pi is the proportion of adults who read while using the toilet. Use a theory-based method to find the rejection region of the test using a significance level of...
According to the 2009 current Population Survey conducted by the U.S. Census Bureau, 40% of the...
According to the 2009 current Population Survey conducted by the U.S. Census Bureau, 40% of the U.S. population 25 years old and over have completed a bachelor's degree or more. Given a random sample of 50 people 25 years old or over, what is the chance that 18 or more has completed a bachelors degree?
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT