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Case Processing Summary Cases Valid Missing Percent PercentTotal PercentHow wrong is itto use marijuana or hashish? Grade Point Average143899.290120.8961450100.09Ho...

Question

Case Processing Summary Cases Valid Missing Percent PercentTotal PercentHow wrong is itto use marijuana or hashish? Grade Point Average143899.290120.8961450100.09How wrong is it to use marijuana or hashish? Grade Point Average Crosstabulation Count Grade Point Average Mostly Ds or FS Mostly Cs Mostly Bs Mostly As Total How wrong is itto use Not wrong at all 14 38 42 12 06 marijuana or hashish? A little bit wrong 70 61 159 Wrong 20 85 120 47 272 Very wrong 39 273 423 166 901 Total 80 466 646 246

Case Processing Summary Cases Valid Missing Percent Percent Total Percent How wrong is itto use marijuana or hashish? Grade Point Average 1438 99.290 12 0.896 1450 100.09 How wrong is it to use marijuana or hashish? Grade Point Average Crosstabulation Count Grade Point Average Mostly Ds or FS Mostly Cs Mostly Bs Mostly As Total How wrong is itto use Not wrong at all 14 38 42 12 06 marijuana or hashish? A little bit wrong 70 61 159 Wrong 20 85 120 47 272 Very wrong 39 273 423 166 901 Total 80 466 646 246 1438 Chi-Square Tests Asymptotic Significance (2-sided) Value 31.364a 28.145 19.020 Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association 000 001 00Q N of Valid Cases 1438 0 cells (0.096) have expected count less than 5. The minimum expected countis 5.90,



Answers

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?

Mhm. So in this case, the Drug Abuse and Resistance Education Program underwent several major changes to keep up the technology and the issues that the students were facing. Now, after all the changes now, there is a school resource officer that think that the proportion of 12 to 17 year olds who have used marijuana in the past six months has decreased. So what would be the null hypothesis the null hypothesis would be then I like hypothesis would be that P is equal to 6.7%. Right, That P is equal to 0.67 And the alternative hypothesis would be the claim of the officer. That P is less than 0.67 which means that he is actually saying that this program is effective. So these would be a null and alternative hypotheses. Now, if the sample data indicate that the null hypothesis should not be rejected, what would the conclusion be then? I like this should not be rejected now. It would mean, uh okay, so after the test is an ally. But this is not rejected. We would say that we do not have. We do not have enough evidence enough evidence to suggest that the proportion of marijuana users users that the proportion off marijuana users in this age group have decreased right. Which means that whatever changes they made to their system, right, whatever changes this program and event, it is not very effective. Okay, now, the party is supposed, in fact, that the proportion of 2017 year olds who have used marijuana is 6.4. Okay, which means that it has actually decreased. But what we did, what we did was we did not reject, right? Uh, yeah, we did not reject the null hypothesis. Have we committed a type one or type two error? Well, the null hypothesis is that P is equal to 6.7% and we have not rejected than the hypothesis, right? Even though the null hypothesis was wrong, even though the true percent is now 6.4% we did not reject the null hypothesis. This means that we have made a type two error a type two ETA. Right? This is going to be the type two error. Why? Whenever you're not hypothesis is wrong. But you failed to reject it. It is always a type tour. These are answers

What we've got to find is what our true positives and negatives, they're simply going to subtract the totals From the false readings. So 143 -24 is 119 and 1 57 -3 is gonna be 154. This means that we had 300 people that were sampled for this. If we just add our totals for the positives and negatives and then for part B were asked of not using marijuana would be uh the results that turned out to be truly negative and then our false positive. So the number that didn't use marijuana would be 154 Plus 24 and we will get 178 Now for the probability that a randomly selected subject did not use marijuana, That would be our previously found number. 178. Yeah, We have 178th out of our 300 MLB 0.593 or 59.3% chance.

The probability is that the person actually used marijuana is going to be our true positive and then we're going to have our false negatives for the ones that are using marijuana and then we'll take the ones that the test selected as well. So this is gonna be um so what we're gonna be looking at is 119 Plus The three from the false negative. And then we're just gonna divide that, bar a total of 300 And this is going to be 0.407. So about 40.7%. And uh it's probably unlikely that the whole population, 40% of the population smokes pot just saying mm

Yeah. Has a percentage of 18-25 year olds using marijuana changed since the publication stating it was 13.6%. Well, our first thing to do is look at the randomly selected people done recently, of the 1283 randomly selected 18-25 year olds, 205 of them said that they currently use marijuana, which is about 16%. Now, in terms of our criteria to see if we can use the one property test are we have to have a simple random sample which we have. And the sample size is so big. That's gonna when we multiply the sample size by our hypothesized population proportion, it's definitely going to be bigger than five. So we are going to go on. Those Are null hypothesis is that our population proportion is 13.6%. And then our alternative hypothesis is going to be the population proportion is not 13.6. See if there has been a change from that last publication. So for our Z score, we're going to have our sample proportion minus the hypothesized population proportion. And I'm plugging in my values here for P zero and for N. And when you run this calculation, you get a Z score of 2.51. And when we looked at him up in the table in the back of the book is the score of 2.51 corresponds to .994. But We're going to subtract that from one. This will give us our high end probability, which is About .006 And then we want not equal to so we actually have to double this because this is a two tailed test, which is going to be .012. Now we are looking at a 5% significance level. This .012 is definitely smaller than .05. So we are going to reject H. O. Which tells us essentially, we have enough evidence to claim. The population proportion of 18-25 year olds using marijuana has changed From the 13.6%. It is not that 13.6% anymore.


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