Please attempt at problem dealing in Chi-Square (Goodness of Fit). Thank you 006Chapter 22 Exercise employment has acualy increased in the past 3 years, or whether the change in empleymens can be...
006Chapter 22 Exercise employment has acualy increased in the past 3 years, or whether the change in empleymens can be explained by random puecruations: What is a Type I error in this case? Whar is a Tipe Il error? 22.8.10 Imagine you are performing a statistical test to determine i Exercise 22.8.1 Sappose someone is trying to sell you a coin that favors heads. You snwch a cotm, but you are skeptical. You test out the coin by flipping it 500 times and ser a p-vatue of 0043. What comclsion can you draw from your finding, and should you buy the com? Exercise 22.8.12 A recent study testing whether this year's SAT scores have improved on average compared to last year has a p-value of 0.031. Is it reasonable to say that more smart people took the SAT this year? Exercise 22.8.14 Your Jfriend Bob is popular on Twitter and is trying to start a YouTube channel. He will devote time to his YouTube career only if at least 40% of his followers subscribe to his channel. After posting a status about his upcoming channel, 3530 of his 8353 followers say they will subscribe. Should Bob start a career on YouTube? Use your knowledge of hypothesis testing to inform Bob ofhis best course of action What are three ways of increasing power? Explain Exercise 22.8.13 Exercise 22.8.15 Imagine that we planted two types of peppers in the garden, which look very similar One is a hot pepper and the other is not so we do not want to confuse them, but we unfortunately forgot to label them. There are an equal number of both ypes. Luckily, the hot peppers are smaller than the sweet peppers. The sizes of both peppers are normally distributed with standard deviation I inch, but the mean length of hot peppers is 3 inches and the mean length of the sweet peppers is 4.5 inches. We randomly pick a pepper Our mull hypothesis is that it is hot. There is a penalty if we misclassify it, since we will put it in the wrong food. If we misclassify it as sweet when it is hot, our utility function is -5. If we misclassify it as hot when it is sweet, our utility is -3. If we correctly classify it, our utility is 10 either way. Set a cutoff that maximizes our utility fuanction for a randomly selected pepper erise 22.8.16 Your friend (who is not the most honest person) claims his die have the following respective probabiliti 20%, 25% and 25% , there 45 6's Should you trust your friend? es for being a 1, 2, 3, 4, 5, or 6: 10% 10% 10% n 200 rolls, there were 15 1's, 20 2's, 22 3's, 45 4's, 53 5's, and Exercise 22.8.11 There are two first exam, the average score for the first class is 84% and the standard probability classes, each with 30 students. On the 99. The second class has an average of 90% with a standard deviation the evidence support the claim that the classes have significantly different mean Comment on the conditions for the test xercise 22.8.18 Prove that as v oo a chi-square distribution with v degrees of 6% Does scores? freedom converges to being normally distributed.
006Chapter 22 Exercise employment has acualy increased in the past 3 years, or whether the change in empleymens can be explained by random puecruations: What is a Type I error in this case? Whar is a Tipe Il error? 22.8.10 Imagine you are performing a statistical test to determine i Exercise 22.8.1 Sappose someone is trying to sell you a coin that favors heads. You snwch a cotm, but you are skeptical. You test out the coin by flipping it 500 times and ser a p-vatue of 0043. What comclsion can you draw from your finding, and should you buy the com? Exercise 22.8.12 A recent study testing whether this year's SAT scores have improved on average compared to last year has a p-value of 0.031. Is it reasonable to say that more smart people took the SAT this year? Exercise 22.8.14 Your Jfriend Bob is popular on Twitter and is trying to start a YouTube channel. He will devote time to his YouTube career only if at least 40% of his followers subscribe to his channel. After posting a status about his upcoming channel, 3530 of his 8353 followers say they will subscribe. Should Bob start a career on YouTube? Use your knowledge of hypothesis testing to inform Bob ofhis best course of action What are three ways of increasing power? Explain Exercise 22.8.13 Exercise 22.8.15 Imagine that we planted two types of peppers in the garden, which look very similar One is a hot pepper and the other is not so we do not want to confuse them, but we unfortunately forgot to label them. There are an equal number of both ypes. Luckily, the hot peppers are smaller than the sweet peppers. The sizes of both peppers are normally distributed with standard deviation I inch, but the mean length of hot peppers is 3 inches and the mean length of the sweet peppers is 4.5 inches. We randomly pick a pepper Our mull hypothesis is that it is hot. There is a penalty if we misclassify it, since we will put it in the wrong food. If we misclassify it as sweet when it is hot, our utility function is -5. If we misclassify it as hot when it is sweet, our utility is -3. If we correctly classify it, our utility is 10 either way. Set a cutoff that maximizes our utility fuanction for a randomly selected pepper erise 22.8.16 Your friend (who is not the most honest person) claims his die have the following respective probabiliti 20%, 25% and 25% , there 45 6's Should you trust your friend? es for being a 1, 2, 3, 4, 5, or 6: 10% 10% 10% n 200 rolls, there were 15 1's, 20 2's, 22 3's, 45 4's, 53 5's, and Exercise 22.8.11 There are two first exam, the average score for the first class is 84% and the standard probability classes, each with 30 students. On the 99. The second class has an average of 90% with a standard deviation the evidence support the claim that the classes have significantly different mean Comment on the conditions for the test xercise 22.8.18 Prove that as v oo a chi-square distribution with v degrees of 6% Does scores? freedom converges to being normally distributed.