Microsoft Word - Exam 4 OL Sp2020 Math12.docx Math 12OL Name___________________________________ Spring 2020 Exam Score: _____________ Exam 3 For problems 1-7, circle the letter next to the response...

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Microsoft Word - Exam 4 OL Sp2020 Math12.docx Math 12OL Name___________________________________ Spring 2020 Exam Score: _____________ Exam 3 For problems 1-7, circle the letter next to the response that best answers the question or completes the sentence. You do not have to show any work or write any explanations here. Make sure to read each statement carefully! (2 pts each) 1. The null hypothesis ( 0H )is a claim about a: A) statistic, where the claim is assumed to be false until it is declared true B) statistic, where the claim is assumed to be true until it is declared false C) parameter, where the claim is assumed to be true until it is declared false D) parameter, where the claim is taken to be false until it is declared true 2. If we get a p-value of 0.011 in a hypothesis test with 2% significance level, then we would A) REJECT the null hypothesis B) NOT REJECT the null hypothesis C) not know whether or not to reject unless we knew if it was a one or two tailed test D) not know whether or not to reject unless we knew the sample size 3. In a hypothesis test, the p-value is: A) the probability of rejecting the null hypothesis when the null hypothesis is true B) the probability of not rejecting the null hypothesis when the alternative hypothesis is true C) the probability of selecting a sample whose test statistic is at least as extreme as the observed test statistic that we got, assuming the null hypothesis is true D) the probability of selecting a sample whose test statistic is at least as extreme as the observed test statistic that we got, assuming the null hypothesis is false 4. We randomly select 20 couples and compare the time the husbands and wives spend watching TV. This is an example of A) independent samples B) paired samples C) none of the above 5. If we fail to reject 0H , then A) we know for certain that 0H is true B) we know for certain that 0H is false C) it is an indication that 0H may be true 6. When constructing a 95% confidence interval for the average math test score difference between all students at two different colleges (Beach College average test scores minus Cabrillo College average test scores), our calculator gives us the interval ( -4.6 , -2.1). This can be interpreted as A) we are 95% confident that Cabrillo College students score between 2.1 and 4.6 points more than Beach College students, on average. B) we are 95% confident that Cabrillo College students score between 2.1 and 4.6 points less than Beach College students, on average. C) we don’t know for certain that it’s a difference in the average math scores since our confidence interval contains 0. D) it is impossible to interpret an interval for a difference of two population means. 7. You can narrow the width of a confidence interval by: A) lowering the confidence level or decreasing the sample size B) lowering the confidence level or increasing the sample size C) increasing the confidence level or decreasing the sample size D) increasing the confidence level or increasing the sample size 8. 10% of all Americans don’t use internet (April 2019). A rural town wants to know if their citizens tend to use internet less than the country average. Suppose we want to test this claim at a 1% significance level. (6 pts) a) State what your null and alternative Hypotheses would be 0H : ____________________ 1H : ____________________ b) If our conclusion is that there is not sufficient evidence to show the citizens of this town uses internet less than the national average, but the truth is that they do, then we have made a A) type I error B) type II error C) correct decision 9. A simple random sample of 28 students was taken at Cabrillo, and they found that 12 of them owned a pet. Are all the assumptions/requirements met so that we could test the claim that more than 30% of all students at Cabrillo owns a pet? Explain why or why not. (3 pts) 10. A study of the weight difference before and after being on Atkins diet for one year, showed that the average weight loss was between 0.56 and 3.64 lbs (4pts) a) Find the point estimate b) Find the margin of error 11. In a hypothesis of the mean using the t-distribution, we got a sample mean with a test statistics t = 2.5. The picture of the corresponding t-curve is shown below, with the area in the right tail calculated (area = 0.0127333). (a) Find the p-value if we are testing 0H : ? = 22 ?# : ? > 22 (b) Find the p-value if we are testing 0H : ? = 22 ?#: ? ≠ 22 For problems 12-15 you need to show all work in order to receive credit! Make sure to clearly state what parameters, formulas and calculator programs you are using. Make sure to use correct symbols! Write your answer using a complete sentence with correct units that indicates that you fully understand the answer. 12. An analysis of the blood of 3,300 people living in Santa Clara county in early April found that 50 of them tested positive for COVID-19 antibodies (indicating that they have prior been infected by the Corona virus). Test the claim that more than 1% of Santa Clara’s population have been infected by the Corona. (We will assume that these test results were correct, which is somewhat disputable at this point still). Use a 2% significance level. (14pts) 1. State the null and alternate hypotheses. 2. State the significance level. 3. Compute the test statistic (by hand). 4. Calculate the p-value. 5. Compare p-value with α and make a decision. 6. Clearly state your conclusion as a full sentence. 13. In a random sample of 31 people who were playing the slot machines the mean age was 48.7 years with a standard deviation of 6.8. In a random sample of 35 people who were playing roulette the mean age was 51.3 years with a standard deviation of 3.2. Use a 1% significance level to test the claim that the average age of those playing the slot machines are younger than those playing roulette. (14pts) 1. State the null and alternate hypotheses. 2. State the significance level. 3. Find the test statistic. 4. Find the p-value. 5. Compare p-value with α and make a decision. 6. Clearly state your conclusion as a full sentence. 14. A researcher wanted to estimate the affect a new drug would have on systolic blood pressure. The following table gives the systolic blood pressures (in mm Hg) of seven adults before taking this drug, and after having taken this drug for 2 months. Before 210 180 195 220 231 199 224 After 195 178 186 223 218 195 224 We will assume that the population of paired differences is approximately normally distributed. (12pts) Construct a 90% confidence interval for the difference in systolic blood pressure before and after taking this drug. 1. Find the point estimate 2. Find the critical value (you can skip this step if you want to) 3. Find the standard error and the margin of error (you can skip this step if you want to) 4. Find the confidence interval 5. Interpret your result. Clearly state which is more or less, and by how much. 15. A researcher is designing an experiment in which rats will navigate a maze. The average time it takes a white rat to complete the