Statistics Trivial Pursuit Solutions (By Color)

Statistics Trivial Pursuit Solutions (By Color)

Blue - Basic Graphs and Descriptive Statistics:

1. Mean, Standard deviation, Min, Max

2. QQ plot, used to check normality of quantitative distributions

3. Shape - bimodal, small gap, Center - peaks are around 33 and 47, Spread - Range is roughly 50

4. Min, Max, Q1, Q3, and the median

5. 1.5 IQR Rule - add 1.5 IQR to Q3, and subtract 1.5 IQR from Q1 - any points outside that are outliers

6. Bar graph/pie chart - no cannot discuss shape for categorical variables

7. Group 1 has a few outliers, but the graphs otherwise look similar, except group 1 is shifted above g2.

8. The standard deviation of 3.4 means that approximately, observations were 3.4 units from the sample mean of 29.2, on average.

9. Basic scatterplot - part of preliminary analysis for a regression analysis.

10. Max, Mean, standard deviation

Pink - Assumptions

1. All expected counts >= 5.

2. Need n1p-hat1, n2p-hat2, n1(1-p-hat1), and n2(1-p-hat2) all >= 10.

3. Need np-hat, and n(1-p-hat)>= 10.

4.The population of differences must be nearly normal or n must be large.

5. The k populations must be normally distributed.

6. The error terms must have a constant variance, and must be normally distributed.

7. The students were randomly selected (via a sampling mechanism) to participate. Additionally, they were asked in such a way that their answers were independent - sets of siblings weren't asked, etc., and students were probably asked alone, so that their peers could not hear their replies and hence adjust their own.

8. Chi-square tests are the easiest example.

9. Either both populations of responses must be nearly normal, or both sample sizes large, or some combination thereof.

10. Sampling less than 10% of the population.

Yellow - Statistical Theory and History

1. The distribution you would obtain by taking all possible random samples of a given size from a population and computing the statistic for all of them.

2. Gossett; Student; Guinness; Quality Control; stout

3. The Central Limit Theorem tells us that for large n, the sampling distribution of the sample mean is roughly normal with a mean equal to the population mean and a standard deviation that is the population standard deviation divided by sqrt(n).

4. Z-scores are computed by taking an observation subtracting the population mean and dividing the result by the standard deviation. They are used to standardize, putting things on the same scale for comparison, and the idea is fundamental for forming many test statistics.

5. standard errors

6. The mean of X+Y=20. The variance of X+Y=9+16=25, so the standard deviation is 5.

7. In homogeneity, there are many populations of interest, while independence only has 1. The questions they are designed to answer are slightly different too - are distributions the same or different (for homogeneity) versus whether or not there is a relationship (independence).

8. Response, nonresponse, and selection

9. 4*2=8 treatments

10. There are a lot of options. Cluster sampling, SRS, Stratified RS, Systematic - look back in Chapter 12 for short descriptions.

Brown - Interpretations

1. The observed slope was 2.14 standard errors below 0.

2. 81% of the variation in the response can be explained by its linear relationship with the predictor.

3. 24/4=6, this is our estimate of roughly how far sample mean values will be from the true mean on average for repeated samples of size 16.

4. A p-value is computed assuming the null is true, but it is not the probability that the null is true.

5. We are 95% confident the true mean weight for the new dog breed lies in (25.2,34.6).

6. s_e is the estimated average size of a residual in the regression. Roughly 3.5 compared to a scale for the y's over 70 units long is really small. So it indicates a good fit.

7. The probability of obtaining an F of 24.56 or larger assuming that there is no difference in population means is .0359.

8. If we generated many 95% confidence intervals, we expect 95% of those intervals to contain the true mean weight of the new dog breed.

9.Conclusions should be in terms of the alternative. We do not have evidence in favor of the alternative hypothesis. This should then be put into additional appropriate context.

10. Assuming the 2 population proportions really are equal, the probability of getting a Z of 1.45 or more or -1.45 or less is .1470.

Green - Last 1/3 Inference

1. The top 2 graphs are ok. The bottom one is where an ANOVA would not be ok.

2. Chi-square GoF

3.The only significant difference in means was found between populations 2 and 3.

4. Regression

5. There is a multiple testing problem if you do the t-tests and do not appropriately lower alpha. Plus, ANOVA can do it all at once, so why do separate tests?

6. Chi-square Independence

7. The alternative hypothesis is directed. You'd have to test for p1>p2 as an alternative.

8. all the samples have the same sample sizes.

9. The p-values in both cases are upper-tailed (to the right). However, the distributions used for each are different. ANOVA is an F distribution, and chi-square uses chi-square.

10. -.9

Orange - Hypothesis Testing Related

1.Power is the probability of correctly rejecting the null when the alternative is true. It can be increased by increasing n or increasing alpha.

2. Probability of rejecting the null when it is in fact true.

3. p-values less than or equal to .035.

4. Stat. sign. means rejected the null. Pract. sign. means the result has meaning to you, stat. sign or not.

5. parametric; nonparametric; many options - Kruskal-Wallis for ANOVA

6. sampling distributions

7. 0

8. It will be very large (> .5). Your p-hat is < .4, so clearly a large p-value.

9. 90%

10. Yes, the entire CI is above 50.