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# RM 17 - To d a y s O u t l i n e Administrative stuff...

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Today’s Outline Administrative stuff Student’s t Confidence intervals The pooled t-test Error ranges Inquiry Four Administrative Stuff FRI Stream allocation notification yesterday Allocation was 69%, 17%, 9%, 4%, 0% for 1st, 2nd, 3rd, 4th, and 5th preferences respectively. Some students from other sections were allocated 5th preferences, or a stream they hadn’t listed. There will be a stream change request form announced soon. Wait until you see what else you are able to register for before requesting a stream change. If you do submit a stream change form, be as specific as you can about what credit you would accept and what streams you would consider. 1 2 3

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Inquiry Four Last week I moved the assignment of Inquiry Four to today However, my highest priority today is getting through the statistics needed for inquiry three. Depending on how long this takes I may or may not get to inquiry four today. I am moving the first week’s requirement for inquiry four to THURSDAY’S LECTURE to remove the time crunch and make sure the inquiry is doable in the time you have left. For this reason, it is IMPORTANT to attend the next lecture. Making things hard to read can boost learning http://www.bbc.co.uk/news/world-11573666 Student’s t The Z-test was for a situation where the population mean μ and standard deviation σ are already known. This is rare. More usually, we do not know μ and σ . We define a new variable Student’s t, similar to z, but using standard error instead of population standard deviation: μ t = x s m = μ x s x n x – μ σ z = μ ) x s x n ( = 4 5 6
The t-distribution is more spread out, flatter than a normal distribution. This is because it is more uncertain. z distribution larger sample t distribution t distribution The spread of the t-distribution is dependent on the sample size. The more samples, the more confident we are that s m is close to σ and the closer t is to z. smaller sample Student’s t is tabulated for different confidence levels, and different “degrees of freedom” (= n – 1) William Sealey Gosset, a.k.a “Student” Chemist & Statistician at: 7 8 9

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We can use the value of student’s t to express a confidence interval We can use student’s t to predict the range in which μ is expected to lie with a given level of confidence. As n increases, the value of t, and hence the confidence interval, decreases, meaning μ will lie within a smaller range. t = μ x s x n Rearranging: μ = ts x n x ± = ± ts m x Confidence Inter val What range contains the true value with a certain confidence level? t-test example one.. = 7.3 ± 5 ( ) (0.4) You measure [Na + ] in chicken noodle soup. For 5 repeat measurements, you calculate your mean and std dev. of 7.3 ± 0.4 mg/mL.
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RM 17 - To d a y s O u t l i n e Administrative stuff...

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