3) While many Americans favor the legalization of marijuana, opponents of legalization argue that marijuana maybe a gateway drug. They believe that if a person uses marijuana, then they are more likely to use other more dangerous illegal drugs. Use the table of random sample data given below and a 5% significance level to test the claim that marijuana users have a higher percentage of other drug use than non-marijuana users. This claim also would indicate that using Marijuana is related to using other drugs. f) Write a sentence to explain the P-value. g) Use the P-value and significance level to determine if the sample data could have occurred by random chance (sampling variability)or is it unlikely to random chance? Explain your answer. h) Should we reject the null hypothesis or fail to reject the null hypothesis? Explain your answer. i) Write a conclusion for the hypothesis test. Explain your conclusion in plain language. j) Is the population proportion related to the categorical variable or not? Explain your answer. | | Uses Other Drugs | Total | |---|---|---| | Uses Marijuana | 87 | 213 | | Does not use Marijuana | 26 | 219 | | | Number of Events | Number of trials | Proportion | |---|---|---|---| | Sample 1 | 87 | 213 | 0.408 | | Sample 2 | 26 | 219 | 0.119 | | Significance Level | Critical Value | Test Statistic Z | p-Value | |---|---|---|---| | 0.05 | 1.645 | 6.850 | 3.6839 · 10?¹² |
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In other words, it measures the strength of evidence against the null hypothesis. g) The P-value is very small (3.6839 10-12), which means that it is highly unlikely to observe such a large difference in proportions between marijuana users and non-users by random Show more…
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33. According to a study conducted in the United States in 2000, 13.6% of all Americans 18-25 years old used marijuana or hashish. In 2007, a random sample of 1,283 Americans of the same age group was interviewed, out of which 205 said that they used these drugs. At the 5% significance level, test whether the data provide sufficient evidence to conclude that the proportion of Americans 18-25 years old that used marijuana and hashish in 2007 had changed since the study of 2000. A) H0: p = 0.136; HA: p ≠ 0.136; z = 2.49; P-value = 0.9872. There is not enough evidence to conclude that the proportion of Americans 18-25 years old that used marijuana and hashish in 2007 had changed since the study of 2000. B) H0: p = 0.136; HA: p ≠ 0.136; z = 2.49; P-value = 0.0128. There is sufficient evidence to conclude that the proportion of Americans 18-25 years old that used marijuana and hashish in 2007 had changed since the study of 2000. C) H0: p = 0.136; HA: p ≠ 0.136; z = 2.49; P-value = 0.0064. There is sufficient evidence to conclude that the proportion of Americans 18-25 years old that used marijuana and hashish in 2007 had changed since the study of 2000. D) H0: p = 0.136; HA: p > 0.136; z = 2.49; P-value = 0.0064. There is sufficient evidence to conclude that the proportion of Americans 18-25 years old that used marijuana and hashish in 2007 had changed since the study of 2000. E) H0: p = 0.136; HA: p ≠ 0.136; z = 2.33; P-value = 0.0198. There is sufficient evidence to conclude that the proportion of Americans 18-25 years old that used marijuana and hashish in 2007 had changed since the study of 2000.
Adi S.
Respondents said it should be made legal. a) Is 62% a sample statistic or a population parameter? Explain. - It is a sample statistic, since it is the observed sample proportion. b) Construct a 95% confidence interval for the proportion of US residents who think marijuana should be made legal, and interpret the interval (in percent in the context of the data. (Round your answers to two decimal places.) - We are 95% confident that approximately 59% to 65% of Americans think marijuana should be legalized. c) A critic points out that this 95% confidence interval is only accurate if the statistic follows a normal distribution, or if the normal model is a good approximation. Is this true for these data? Explain. - The sample is random and comprises less than 10% of the American population, therefore we can assume that the individuals in this sample are independent of each other. The number of successes is 620 and the number of failures is 380, so the success-failure condition is met. Therefore, the distribution of the sample proportion is expected to be approximately normal. d) A news piece on this survey's findings states, "Majority of Americans think marijuana should be legalized." Based on your confidence interval, is this news piece's statement justified? - Yes, because the interval does not contain 50%, suggesting that the true proportion could be 50% or higher.
Jerelyn N.
According to the Centers for Disease Control and Prevention, in $2001,10.2 \%$ of high school students had tried marijuana for the first time before the age of $13 .$ The Drug Abuse and Resistance Education (DARE) program underwent several major changes to keep up with technology and issues facing students in the 21st century. After the changes, a school resource officer (SRO) thinks that the proportion of high school students who have tried marijuana for the first time before the age of 13 has decreased from the 2001 level. (a) Determine the null and alternative hypotheses. (b) Suppose sample data indicate that the null hypothesis should not be rejected. State the conclusion of the SRO. (c) Suppose, in fact, the proportion of high school students who have tried marijuana for the first time before the age of 13 was $9.5 \% .$ Was a Type I or Type II error committed?
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