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1. A survey in the United States stated that ˆp = 56% of the 600 randomly selected Kansas residents planned to set off fireworks on the fourth of July. • Check the independence and success/failure conditions. Are there any assumptions we need to make to use the Central Limit Theorem? • Calculate the margin of error (ME) based on a 95% confidence interval. • Construct a 95% confidence interval to determine where we expect the target population to fall 95 times out of 100 times. • Suppose p = 60% of all Kansas residents set off fireworks on the fourth of July. Based on your 95% confidence interval, is our sample population different from our target population? 2. Researchers collect data on 25 Vancouverites. It is found that, on average, they sleep 7.73 hours per night with a sample standard deviation of sx = 0.77. We would like to test the hypothesis that Vancouverites sleep less than 8 hours per night. • Write the hypotheses in symbols. • Check the independence and sample size conditions. Are there any assumptions we need to make to use the Central Limit Theorem? • Calculate your test statistic, degrees of freedom and probability-value. You do not need to create a confidence interval. • What reasonable conclusion can we make based on our probability-value? 3. A group of 44 patients were randomly divided evenly into two groups. The treatment group ate lunch while watching a football game on television. The control group ate lunch without any added distractions. On average, patients in the treatment group ate x1 = 52.1 grams of food with a standard deviation of s1 = 45.1 grams. On averge, patients in the control group ate x2 = 27.1 grams of food with a standard deviation of s2 = 26.4 grams. We would like to test the hypothesis that food intake was different between the two groups. You may assume all conditions are met to use the Central Limit Theorem. • Write the hypotheses in symbols. • Calculate your test statistic, degrees of freedom and probability-value. You do not need to create a confidence interval. • What reasonable conclusion can we make based on our probability-value? 4. At March 18, 2020 around 11:15am, Bryan checked the death counts caused by COVID19 for China and Italy. The information is presented in the table below. We are going to test the hypothesis that the proportion of deaths in China is different from the proportion of deaths in Italy. You may assume all conditions are met to use the Central Limit Theorem. Country Total Cases Total Deaths Total Recovered Active Cases China 80,894 3237 69,614 8043 Italy 35,713 2987 4025 28,710 • Create point estimates ˆp1 and ˆp2 for the proportion of total deaths to total cases (ie. divide the total deaths by the total cases for each country). Round your proportions correctly to four decimal places. • Use ˆp1 and ˆp2 to calculate ˆp and SEpool. You should round ˆp and SEpool correctly to four decimal places. • Write the hypotheses in symbols. Use the Normal CD function and a two-tailed test, to show that there is very strong evidence to reject H0. You do not need to create a confidence interval. • Why might our conclusion that China and Italy seem to have different death rates not be a reasonable conclusion? 5. A casino game involves rolling a six-sided die three times in a row and counting up the number of 6s we obtain. Notice that we can model this problem using a Binomial distribution with X representing the number of 6s we roll (0, 1, 2 or 3). (i). Using the Binomial PD function on your calculator, determine the expected probability values for the distribution: X F(X) 0 1 2 3 (ii). A gambler comes into the casino and plays 100 times. The observed values are summarized below. Fill in the number of expected rolls by multiplying your f(x) values in (i) by 100 X Observed Rolls Expected Rolls 0 48 1 35 2 15 3 2 iii). Use a goodness of fit test to determine if the casino should kick out the gambler or not. That is, are his observed rolls similar to what we would expect, or different enough for us to be suspicious? Be sure to check any conditions to be able to use the chi-square distribution. If you need more space, you can continue on the back of this page. 1. A survey in the United States stated that ˆp = 56% of the 600 randomly selected Kansas residents planned to set off fireworks on the fourth of July. • Check the independence and success/failure conditions. Are there any assumptions we need to make to use the Central Limit Theorem? • Calculate the margin of error (ME) based on a 95% confidence interval. • Construct a 95% confidence interval to determine where we expect the target population to fall 95 times out of 100 times. • Suppose p = 60% of all Kansas residents set off fireworks on the fourth of July. Based on your 95% confidence interval, is our sample population different from our target populatio n? 2. Researchers collect data on 25 Vancouverites. It is found that, on average, they sleep 7.73 hours per night with a sample standard deviation of sx = 0.77. We would like to test the hypothesis that Vancouverites sleep less than 8 hours per night. • Wri te the hypotheses in symbols. • Check the independence and sample size conditions. Are there any assumptions we need to make to use the Central Limit Theorem? • Calculate your test statistic, degrees of freedom and probability - value. You do not need to cre ate a confidence interval. • What reasonable conclusion can we make based on our probability - value? 3. A group of 44 patients were randomly divided evenly into two groups. The treatment group ate lunch while watching a football game on television. The control group ate lunch without any added distractions. On average, patients in the treatment group ate x1 = 52.1 grams of food with a standard deviation of s1 = 45.1 grams. On averge, patients in the control group ate x2 = 27.1 grams of food with a standard deviation of s2 = 26.4 grams. We would like to test the hypothesis that food intake was different betwee n the two groups. You may assume all conditions are met to use the Central Limit Theorem. • Write the hypotheses in symbols. • Calculate your test statistic, degrees of freedom and probability - value. You do not need to create a confidence interval. • What reasonable conclusion can we make based on our probability - value? 4. At March 18, 2020 around 11:15am, Bryan checked the death counts caused by COVID19 for China and Italy. The information is presented in the table below. We are going to test the hypothesis that the proportion of deaths in China is different from the proportion of deaths in Italy. You may assume all conditions are met to use the Central Limit Theorem. Country Total Cases Total Deaths Total Recovered Active Cases China 80,894 3237 69,614 8043 Italy 35,713 2987 4025 28,710 • Create point estimates ˆp1 and ˆp2 for the proportion of total deaths to total cases (ie. divide the total deaths by the total cases for each country). Round your proportions correctly to four decimal places. • Use ˆp1 and ˆp2 to calculate ˆp and SEpool. You should round ˆp and SEpool correctly to four decimal places. • Write the hypotheses in symbols. Use the Normal CD function and a two - tailed test, to show that there is very strong evidence to reject H0. You do not need t o create a confidence interval. • 1. A survey in the United States stated that ˆp = 56% of the 600 randomly selected Kansas residents planned to set off fireworks on the fourth of July. • Check the independence and success/failure conditions. Are there any assumptions we need to make to use the Central Limit Theorem? • Calculate the margin of error (ME) based on a 95% confidence interval. • Construct a 95% confidence interval to determine where we expect the target population to fall 95 times out of 100 times. • Suppose p = 60% of all Kansas residents set off fireworks on the fourth of July. Based on your 95% confidence interval, is our sample population different from our target population? 2. Researchers collect data on 25 Vancouverites. It is found that, on average, they sleep 7.73 hours per night with a sample standard deviation of sx = 0.77. We would like to test the hypothesis that Vancouverites sleep less than 8 hours per night. • Write the hypotheses in symbols. • Check the independence and sample size conditions. Are there any assumptions we need to make to use the Central Limit Theorem? • Calculate your test statistic, degrees of freedom and probability-value. You do not need to create a confidence interval. • What reasonable conclusion can we make based on our probability-value? 3. A group of 44 patients were randomly divided evenly into two groups. The treatment group ate lunch while watching a football game on television. The control group ate lunch without any added distractions. On average, patients in the treatment group ate x1 = 52.1 grams of food with a standard deviation of s1 = 45.1 grams. On averge, patients in the control group ate x2 = 27.1 grams of food with a standard deviation of s2 = 26.4 grams. We would like to test the hypothesis that food intake was different between the two groups. You may assume all conditions are met to use the Central Limit Theorem. • Write the hypotheses in symbols. • Calculate your test statistic, degrees of freedom and probability- value. You do not need to create a confidence interval. • What reasonable conclusion can we make based on our probability-value? 4. At March 18, 2020 around 11:15am, Bryan checked the death counts caused by COVID19 for China and Italy. The information is presented in the table below. We are going to test the hypothesis that the proportion of deaths in China is different from the proportion of deaths in Italy. You may assume all conditions are met to use the Central Limit Theorem