Registered Sec Name Thursday Sec TAMUSTAT Homework 6 1 As we keep tossing a coin as n increases which of the following happens A The sample proportion p gets smaller No the sample proportion p will flucuate about the true proportion so it could get smaller OR larger assuming it is a random sample Although p x n as n increases so does x so p s size stays relatively the same B The sample proportion p gets closer to the population proportion Yes the larger the sample the closer the estimate p is to the true parameter value C The standard deviation of the sample proportion p gets smaller Yes p 1 n so as n increases p decreases D All of the above will happen No obviously E Only two of the above will happen Yes B and C 2 Why use or report an average of several observations instead of just one A You could have made a mistake with one but it s less likely you d make the same mistake with several No Although this might be a true statement it is not the reason we use the mean Notice you could be taking biased observations so the mean would also be biased you d be making the same mistake B The average is less biased than any individual observation No both the means x s and the observations x s are unbiased they re mean is C An average can t be an outlier No a sample mean can be an outlier but it will still be closer to than some of the x s Notice the outlier in both of the boxplots for the sample means in HW3 2 D Averages are less variable than the individual observations Yes x x n so the sample means will always be les variable than the x s unless n 1 then it would be the same E An individual observation can t represent the mean of a whole population No since the x s are unbiased any of them COULD represent the population they just wouldn t be very good representatives 3 Assuming the graph above represents the probability distribution for X what is P 0 5 X 1 0 P 0 5 X 1 0 0 5 1 0 0 5 0 5 0 125 1 2 base height A 0 5 B 0 125 C 0 25 D 0 375 E 0 625 4 For the same distribution what is P X 0 5 X is a CONTINUOUS variable therefore the probability that It EQUALS anything is ALWAYS 0 A 0 B 0 375 C 0 5 D 0 25 E 0 125 5 What is the 79th percentile for the standard normal Z N 0 12 P Z z 0 79 looking up 0 79 in the body of the table you ll find z 0 81 A 0 79 B 0 7852 C 0 2148 D 0 81 Registered Sec Name Thursday Sec TAMUSTAT E 0 81 6 Let X N 25 42 What is P 20 X 26 P 20 X 26 P 20 25 4 Z 26 25 4 P 1 25 Z 0 25 P Z 0 25 P Z 1 25 0 5987 0 1056 0 4931 A 0 4931 B 0 7043 C 0 4013 D 0 8413 E 0 6853 7 We ve talked alot about describing a distribution What does this mean A It means we need to know the 5 Number Summary No this gives us an idea of the shape center and spread but we need the actual distribution e g normal or uniform and B It means we need to know that the data is normal No this is not enough C It means we need to know the shape maximum and minimum No the minimum and maximum don t give us plus we also need the mean D It means we need the shape center and spread Yes this gives us the distribution shape mean center and standard deviation spread so we can find probabilities E It means we need to know the mean and the median since we can then tell if the distribution is symmetric or skewed left or right No we still need actual distribution and the standard devation 8 Let X 9 N 5 22 What is the range of the middle 90 of these X 9 What are xa and xb such that P xa X 9 xb 0 90 centered at the mean 5 We must find the z s first and convert to X 9 P z Z z 0 90 P Z z 0 95 and P Z z 0 05 z 1 645 xa z 5 1 645 2 1 71 and xb z 5 1 645 2 8 29 A 1 71 8 29 B 1 645 1 645 X9 These are the z s but we need to convert to C 8 29 8 29 This is not centered at the mean 5 D 1 28 1 28 This is not centered at the mean 5 E 2 44 7 56 This is centered at the mean 5 but it is too wide 9 If I had asked for the middle 95 instead whichof the following would be true A The interval would be wider since the standard deviation would be larger No changing the percentage only changes the z s not the standard deviation B The interval would be narrower since the standard deviation would be smaller No changing the percentage only changes the z s not the standard deviation C The interval would be wider since it covers more of the possible observations Yes increasing the percentage increases the z s therefore making the interval wider D The interval would be narrower since it smore accurate No the interval would be wider E The interval would be the same since the mean and standard deviation would not change No the z s change 10 When is a sample size of 30 not enough to say the distribution of approximately normal A when the data is categorical and the true proportion of successes is less than 15 Registered Sec Name Thursday Sec TAMUSTAT Yes the rule for categorical data is n and n 1 5 If 0 15 n 30 0 15 4 5 which is 5 B when the data is already normal No 30 is actual more than what we need When the data is normal the sample mean is also normal now matter what n is used C when the data is highly skewed Yes for highly skewed data extremely NONnormal 30 is not enough for the sample means to be consistently normally distributed D All of the above are true statements No E Exactly two of the above are true statements 11 Let p42 N 0 7 0 0712 What is P p42 0 5 P p42 0 5 P Z 0 5 0 7 0 071 P Z 2 82 0 0024 A 0 5 B 0 C 0 9976 D 0 0024 E 0 2 12 Why do we call the distribution …