Introduction to Mathematical Statistics
Introduction to Mathematical Statistics STAT 310
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Mrs. Triston Collier
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This 2 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 310 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 32 views. For similar materials see /class/205086/stat-310-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.
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Date Created: 09/17/15
TA Yi Chai Of ce 1335N MSC Email Webpage Of ce Hours STAT 310 DISCUSSION 8 chaiyistat wiscedu 1 Con dence Intervals httpwwwstatwisceduchaiyi 1100 1200pm T and 100 200pm Th or by appointment 10017 a CI Margin of error Length of 01 known 02 l7 i 2042 x i 2042 x 1 22042 x i 771 771 771 mean of Nu7 02 f8 f8 f8 unknown 02 Y i tutMRI x W tutMRI x W 2ta2 11 x W Proportions A A17 pizaZ p 71 2042 n 031 22042 n 2 Sample size calculation 0 Estimation of mean of a normal distribution Nu7 02 with known a The sample size n such that the margin of error for the 1 7 04 con dence interval for u is no greater than a prescribed value 6 is ZDL n 2 U i 0 Estimation of proportion The required sample size is 3 Examples 0 Example 1 6310 from the textbook How many times must we toss a coin to ensure that a 095 con dence interval7 for the probability of heads on a single toss7 has length less than 017 005 and 0017 respectively 0 Example 2 6312 from the textbook Suppose that a measurement on a population can be assumed to be distributed Nu7 2 where u is unknown and that the size of the population is very large A researcher wants to determine a 095 con dence interval for u that is no longer than 1 6 1 Zea2 2 n 2 17 2 What is the minimum sample size that will guarantee this 0 Example 3 6315 from the textbook Generate 103 samples of size n 5 from the Bernoulli05 distribution For each of these samples7 calculate 636 221722 221722 7 2172 Tv 7 t 2172 T with 39y 095 and record the proportion of intervals that contain the true value What do you notice Repeat this simulation with n 20 What do you notice S number of simulation n sample size simu lt functionSnp num0 for simno in 18 xrbinomn1p hatpsumxn lowerhatp196sqrthatp1hatpn upperhatp196sqrthatp1hatpn if lowerltp amp uppergtp numnum1 returnnum simu1000505 simu10002005 0 Example 4 6316 from the textbook Generate 104 samples of size n 5 from the N01 distribution For each of these samples7 calculate the interval lt22 7 8N5 32 5N5 where s is the sample standard deviation7 and record the proportion of times this interval contains 1 0 Repeat this simulation With n 10 and 100 Compare your results simu lt functionSn num0 for simno in 18 xrnormn lowermeanxsdxsqrtn uppermeanxsdxsqrtn if lowerlt0 amp uppergt0 numnum1 returnnum simu100005 simu1000010 simu1000020
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