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Hypothesis testing Step 1: State hypothesis In plain EnglishStep 6: Selec test statisticStep 7: Critical valueStep 2: Select the statistica measureStep 8: Compute t...

Question

Hypothesis testing Step 1: State hypothesis In plain EnglishStep 6: Selec test statisticStep 7: Critical valueStep 2: Select the statistica measureStep 8: Compute the test statisticStep 3: One-side or two-side?Step 4: State hypothesis mathStep 9: Compare the test calculated with the critical valueStep 5: Level of testStep 10: Write conclusion

Hypothesis testing Step 1: State hypothesis In plain English Step 6: Selec test statistic Step 7: Critical value Step 2: Select the statistica measure Step 8: Compute the test statistic Step 3: One-side or two-side? Step 4: State hypothesis math Step 9: Compare the test calculated with the critical value Step 5: Level of test Step 10: Write conclusion



Answers

Instructions: For the following ten exercises, Hypothesis testing: For the following ten exercises, answer each question.
a. State the null and alternate hypothesis.
b. State the p-value.
c. State alpha.
d. What is your decision?
e. Write a conclusion.
f. Answer any other questions asked in the problem.
According to the Center for Disease Control website, in 2011 at least 18% of high school students have smoked a cigarette. An Introduction to Statistics class in Davies County, KY conducted a hypothesis test at the local high school (a medium sized–approximately 1,200 students–small city demographic) to determine if the local high school’s percentage was lower. One hundred fifty students were chosen at random and surveyed. Of the 150 students surveyed, 82 have smoked. Use a significance level of 0.05 and using appropriate statistical evidence, conduct a hypothesis test and state the conclusions.

Oh, welcome to the video. And today we'll be talking about how offices tests and specifically how to know when our evidence does or does not sufficiently support our claim. So this problem, we're told that it is proposed. The average amount of rainfall for the Northeastern U. S is at least 11.52 inches. So we can translate this into a null hypothesis by saying that new or the population mean rainfall is equal or not. Sorry, not equal to is greater than or equal to, because the problem where did it as at least 11.52 inches. However, it is suspected that this figure is too high, so we can make an alternative hypothesis by saying that mu is actually less than the proposed value. So if we want to visualize this, let's say we have ah, poorly drawn distribution here with a peak value at the proposed I'm sorry. That should say mu is equal to 11.52 and it is proposed that the true value of Mu is either at or greater then this value here. But with our hypothesis tests, we'd like to find evidence to show that the true value is actually somewhere over here. So in other words, will be doing a left tailed test and we'll be testing these hypotheses at the 5% L. So, um, to test these hypotheses, we we conduct a sample of 10 cities and of these 10 cities, we find an average, um sample mean, uh, rainfall of 7.42 inches with the sample standard deviation of 1.3 inches. So, um, with that information here, we can say with this information that we learned from our sample and the information that we're getting from the problem on this slide here, we can go to our calculators to find ourselves a testes tick and corresponding p value. So if we go to our calculators, I'm using a T I 84 plus and we go to the T test function, and I give it these parameters here. So, mu um, which is just what's being proposed here is 11.52 The X bar is what we find here, which is 7.42 That is a terrible too. But that is a two with a sample standard deviation of 1.3 and a sample size of 10. We hope to find a value that is less than what is proposed. So if you give it all this information here and press enter were given a test statistic or in this case, a t value of negative 9.97 which is really, really big and a corresponding p value of essentially zero. So we can see that this is very statistically significant. And we can see that R P value is clearly less than our Alfa level of 5% 0.5 and therefore, our evidence is telling us to reject the no hypothesis. So in other words, we do have sufficient evidence to show that the claim that the average rainfall off the Northeastern U. S. Is at least 11.52 we do have enough evidence to show that this is most likely wrong. At the end of the day, we we reject the null hypothesis and argue in favor off the alternative

Oh, welcome to the video. And today we'll be talking about hypothesis tests specifically how to know when our evidence it does or does not sufficiently support our claim. So this problem, we're told that, um, is proposed that the proportion of fatal automobile accidents caused by driver error is 54%. So we can translate that into a no hypothesis here by saying that ex, which is just what we're gonna call this proportion is equal 2 54% or 0.54 And it is there is suspicion regarding this proportion here. And people don't think that this is accurate anymore. So we can translate that into an alternative hypothesis by saying that X does not equal 0.54 So if we want to visualize this, let's say we have ah distribution here. With a peak value at the proposed 54% we would like to find evidence in this hypothesis test that shows that X, instead of being around here, is actually somewhere over here. We're somewhere over here, but more most importantly, not close to 0.54 So, in other words, this will be a two tailed hypothesis test and we will be doing this hypothesis test at the 5% healthy level. So to test these hypotheses, a sample of 30 automobile accidents were collected, and out of the 30 it was shown there, it was found that 14 of the 30 were caused by a driver error. So with this information that we get from our sample and the information we're given from the problem, we can find a test statistic and a resulting P value. So if we go to our calculators, I'm using a T I 84 plus and we go to the one proportions Easy test function when we give it these parameters here. So the proposed proportion is 54%. The amount of success is this case. Is the descriptions just called X in the calculator? Um, so in the context of the problem, the amount of accidents that were caused by driver error, it's 14 out of a sample size of 30. And we're telling the calculator that we are looking for ah, value that does not equal the propose value of 54%. So if we give it all this information here and for us to enter it gives us a Z statistic Z score of negative 0.5. Um, actually, no, no, that's not right. Um, that is your 0.5, but looks like zero point 81 negative. 0.81 is our test statistic, and this translates into a P value of 0.42 And as we can see are calculated. P value is not less than our Alfa level, and therefore, our evidence tells us that we should fail to reject the null hypothesis. So in the context of the problem, we do not have sufficient evidence to prove that 54% is an inaccurate representation of the proportion of automata automobile accidents caused by driver air. So at the end of the day, we failed to reject the null.

Hello. Welcome to the video, and today we'll be talking about have offices, tests and specifically how to know when our evidence does or does not sufficiently support our claim. So in this problem it is proposed that, um, women visit their act there, Doctor, on average at most, uh, 5.8 times per year. So we can translate this into a null hypothesis by saying that mu, or the average amount of times a woman visits her doctor per year is less than or equal to 5.8. And this is the case because the problem told us at most 5.8. And it is suspected that this is actually not right and that the true value of me was actually greater than was proposed. So we can translate that into alternative have offices by saying that Mu is greater and 5.8. So if we want to visualize this, let's say we have ah distribution right here with a proposed or with a peak value at the proposed five point days, and we're being told that the true value of Mu is either at or less than 5.8. So somewhere in this area. We'd like to find evidence to show true value of mu. It's actually somewhere over here. So in other words, will be doing a right tailed test and we'll be testing these hypotheses at you 5% Alfa level. So, uh, to, uh, assess these hypotheses. A sample of 20 women is collected, and, uh, the amount of times each woman visits the doctor. Her year is collected, and your textbooks should give you those 20 values. So if we create a list in our calculators, I'm using a T I 84. Plus, um, if we create a list of those 20 values and our calculators and we go to the T test function and we give it these parameters, we tell it that the proposed value of mu is equal to 5.8. And, um, whatever, whatever. Wherever you store the values for a list, that's just where you tell it. Greeting retell it it is. And we always keep frequency at one. We don't have to worry about this value pretty much, and we're hoping to find a value that is greater than what is proposed to give it all this information here and press enter. Ah, we go or we're given a test. A tous tick off. Um T t score of negative 3.8. I'm sorry. 3.4 with a corresponding p value of zero point 99 Essentially, it's pretty close to one. So as we can see right here, R p value is not very significant. And we can see that r p value is clearly not less than our Alfa level. And therefore, our evidence is telling us to fail to reject the null hypothesis. So in the context of the problem, we do not have enough evidence to essentially prove that 5.8 is too is an inaccurate value from you. Um, it might be an inaccurate value, but our evidence does not give us enough substantiation or support for this claim right here. So as it stands right now, we failed to reject the no


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