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This lab session will serve as a reminder for the upcoming first midterm exam and review important concepts such as probability, random variables, sampling distributions, confidence intervals, and hypothesis testing.
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Stat 350 Lab SessionGSI: Yizao WangSection 016 Mon 2pm30-4pm MH 444-DSection 043 Wed 2pm30-4pm MH 444-B
Outline • First midterm exam reminder • Big ideas review • Qwizdom and non-qwizdom review questions • In lab project (ILP) on proportion Today’s Qwizdom question is anonymous, you don’t have to login with your UMID.
First Midterm Exam • 14th Feb. 6pm-7pm30 1324 EH • Material: Ch. 1, 2, 3, 4, 7, 8, 9.1-9.4, 10.1-10.3, 12.1-12.3, 12.5HW 1-4 and all lab material • Bring: PICTURE ID, Pen/pencils, erasers, and a calculator. Formula cards with tables will be provided with the exam. • Alternate, randomized seating will be used in the exam rooms. • No cell phones, beepers, palm pilots allowed in the exam rooms. • All bags/backpacks will be placed against the exam room wall, so the less extra things you bring, the better.
Data • We’ve talked about two broad types of data this semester • Do you remember what they are?
Probability • We learned several rules for calculating probabilities of events • E.g. the event ‘Tails’ in the flip of a fair coin • Special relationships between two events • Mutually exclusive • Independent • Could you provide definitions and examples of each?
Random Variables • We’ve talked about two types of random variables • Can you name them? • We’ve talked about three different models (i.e. distributions) for random variables • Can you describe them (be specific)? • Can you find probabilities under each? • Do you know which model is appropriate for each type?
Sampling Distribution of p-hat • Can you describe what the sampling distribution of p-hat is? • Do you know when to use it? • When the problem asks you to find a probability for a sample proportion • When the sample size is large enough: np≥10, n(1-p) ≥10
Confidence Intervals for p • Useful when we want to provide a range of reasonable estimates for the population proportion • Do you know how to interpret the confidence level? • Do you know how to use a confidence interval to make a decision, and under what conditions this would be appropriate?
Hypothesis Testing for p • Useful for making a Yes/No type decision about particular value(s) of a population proportion • Do you know the 5 steps of hypothesis testing? • Can you interpret and calculate a test statistic? • Can you interpret and calculate a p-value?
If your p-value is significant at the 5% level, then it will also be significant at the … • 1% level • 10% level • Both of the above • None of the above
True or False The standard error of p-hat estimates, roughly, the average distance of an observed p-hat value from the true population proportion.
I tell you “A and B are mutually exclusive.” Choose all of the true statements below. • A and B are independent • P(A and B) = 0 • P(A and B) = P(A)P(B) • P(A or B) = P(A) + P(B) • None of the above are true
X has the Bin(n,p) distribution. How would you find P(p-hat>0.2)? Choose all that apply... • Use sampling distribution of p-hat to find P(p-hat > 0.2) directly • Use normal approximation to binomial to find P(X > 0.2*n) instead • Not enough information
Which of the following distributions for X meet the criteria to use the normal approximation? Choose all that apply... Binomial(25, 0.2) Binomial(25, 0.5) Binomial(25, 0.7) None of the above
Which graph(s) would be appropriate to display a quantitative variable? Choose all that apply... Bar chart Histogram Boxplot QQ-plot Time-series plot
Which graph(s) would be appropriate to display shape of a distribution? Choose all that apply... Histogram Boxplot QQ-plot Time-series plot
A well constructed survey of monkeys found that 75% of monkeys with prehensile tails prefer bananas to grubs. Express this as a conditional probability. P(prehensile tail | prefer bananas) = 0.75 P(prefer bananas | prehensile tail) = 0.75
To determine if monkey tail status (prehensile or not) is independent of food preference (bananas or grubs), we could compare P(prefer bananas | prehensile tail) to… P(prehensile tail | prefer bananas) P(prehensile tail) P(prefer bananas)
A 95% confidence interval will be ________ a 99% confidence interval. Narrower than Wider than The same as Can’t tell
Discrete Continuous Normal(μ,σ) Uniform(a,b) Binomial(n,p) Match the type of random variable to the appropriate distribution(s)
True or False A z-statistic tells you how many standard errors your observed sample proportion is from the true proportion.