1. A random sample is one ______ a. That is haphazard b. That is unplanned c. In which every unit of a particular size has an equal probability of being selected d. That ensures that there will be no uncertainty in the 2. 10 students participate in Statistics quiz 2, their grades are: 98, 85,89,73,76,85,87,92,85,56 WHAT ARE THE: MEAN, MEDIAN, MODE, RANGE, VARIANCE, STANDARD DEVIATION, INTER-QUARTILE RANGE (IQR) 3. For the scores 3, 5, 8, 10, 14, 17, 21, 25, calculate the 75 th percentile using the following formula: R = P/100 x (N + 1) (BE CAREFUL IT'S NOT (a)) a. 6.75 b. 17 c. 21 d. 20 4. FOR THIS BOX PLOT TELL WHAT EACH LETTER (A - H) REPRESENTS: 5. A box of marbles contains: 20 red, 10 green, 12 yellow and 8 blue. After shaking the box, we randomly select 5 marbles WITHOUT REPLACEMENT (THIS IS IMPORTANT). What is the probability that the first is RED, the second is RED, the third is GREEN, the fourth is Yellow and the fifth is BLUE. (the two reds make this tricky) 5. If you throw a six sided die twice, what is the probability that you will get: (a) A one on the first throw OR a two on the second throw ? (b) A one on the first toss AND a two on the second toss of the die ? 6. Here are five letters: A, F, G, T, S (a) How many 3-letter COMBINATIONS can you make from these 5 letters? (b) How many 3-letter PERMUTATIONS can you make from these 5 letters? (c) Would either number change if the \"S\" were replaced with a second \"F\"? 7. Consider a normal distribution with a mean of 25 and standard deviation of 4. Approximately, what proportion of the area lies between values of 17 and 33. a. 95% b. 68% c. 99% d. 50% 8. Convert the two x-values (raw data points 17 and 33) to standardized z-values and what are they? What is the standardized mean? IF YOU GOT THIS ONE RIGHT, THEN YOU CAN SEE WHY WE USE AN ALPHA OF 5% TO SEPARATE THE PROBABLE FROM THE IMPROBABLE (WHERE WE REJECT THE NULL HYPOTHESIS FOR EXAMPLE, OR CONSIDER A VALUE \"UNUSUAL\") REFER BELOW TO THE TABLE OF Z-SCORES (or find one on the web) AND CORRESPONDING AREAS UNDER THE NORMAL CURVE FOR THE FOLLOWING QUESTIONS (IGNORE THE CIRCLED VALUES). REMEMBER THAT Z-SCORES ARE THE NUMBER OF STANDARD DEVIATIONS FROM THE MEAN AND THAT FOR NORMALLY DISTRIBUTED DATA (LIKE THE MEANS OF SAMPLE MEANS) ABOUT 95% OF THE DATA FALL BETWEEN + 2 STANDARD DEVIATIONS FROM THE MEAN. 9. FOR A Z-VALUE OF +2.00 (TWO STANDARD DEVIATIONS) WHAT IS THE AREA (FROM THE TABLE ON THE RIGHT) THAT REPRESENTS THE PERCENT OF DATA TO THE LEFT OF IT? NOW, WE MUST SUBTRACT THE SHADED AREA IN THE LEFT TAIL (GRAPH AND TABLE ON THE LEFT) AT Z = -2.00 FROM THIS LARGER AREA TO GET THE TOTAL PERCENT OF OUR DATA THAT IS WITHIN +2 STANDARD DEVIATIONS FROM THE MEAN. WHAT IS THIS RESULTING AREA (TO 4 DECIMAL PLACES 0.0000) ? LET'S MOVE ON TO QUESTIONS ON HYPOTHESIS TESTING. (e.g., testing whether or not our sample reflects the true population statistic like the mean? There are other things we can test as you have done, but it all comes back to the above z-table or the t-Table with n-1 df) 10. We have a null hypothesis Ho and an alternate hypothesis Ha, which have to account for all possibilities. AND the null hypothesis MUST have the \"equals\" in it (not in the Ha) So, if Ho: u > 50 then Ha is: u < 50 Is this a right, left or two-tailed hypothesis test? If Ho: u = 32 and Ha: u 32 Is this a right, left, or two-tailed hypothesis test? IF we have the population mean AND STANDARD DEVIATION, we can use the z-Table for a Normal Distribution IF we have the population mean BUT NOT ITS STANDARD DEVIATION, we must use the t-Table and know the sample size to get the n-1 degrees of freedom. As the n increases (to about 1000) the shape of the t-Distribution gets wider and looks more and more like the Normal Distribution and the tTable values get approximately the same as the z-Table values. For a hypothesis test we must assume a significance level (PROBABILITY), alpha, that we will use to accept or reject our null hypothesis. The most common alpha is 5%, meaning that 5% (0.05) of the area under the Normal graph is to the RIGHT of a specific \"critical\" +z-score or +z-value for a RIGHT TAILED (+) test. If our calculated test statistic (calculated z-zcore) is LARGER THAN the critical +zscore, we are in the \"rare\Value 98 85 89 73 76 85 87 92 85 56 Descriptive Summary Variable Mean Median Mode Minimum Maximum Range Variance Standard Deviation Coeff. of Variation Skewness Kurtosis Count Standard Error 82.6 85 85 56 98 42 138.4889 11.7681 14.25% -1.2887 2.2295 10 3.7214 Mean Median Mode Range Variance Standard Deviation IQR Variable 82.6 85 85 42 138.48889 11.76813 10.25 3 5 8 10 14 17 21 25 98 85 89 73 76 85 87 92 85 56 3 5 8 10 14 17 21 25 20 Descriptive statistics count mean sample variance sample standard deviation minimum maximum range 1st quartile median 3rd quartile interquartile range mode low extremes low outliers high outliers high extremes Value 10 82.60 138.49 11.77 56 98 42 78.25 85.00 88.50 10.25 85.00 0 1 0 0 Normal Probabilities Common Data Mean Standard Deviation 25 4 Probability for a Range From X Value To X Value Z Value for 17 Z Value for 33 P(X<=17) P(X<=33) P(17<=X<=33) 17 33 -2 2 0.0228 0.9772 0.9545 0.02777778 0.33333333 4 24 125 0.0228 0.0456 71292E+013 0.36 49.04 -2.575829 0.001434801 Value 98 85 89 73 76 85 87 92 85 56 Descriptive Summary Variable Mean Median Mode Minimum Maximum Range Variance Standard Deviation Coeff. of Variation Skewness Kurtosis Count Standard Error 82.6 85 85 56 98 42 138.4889 11.7681 14.25% -1.2887 2.2295 10 3.7214 Mean Median Mode Range Variance Standard Deviation IQR Variable 82.6 85 85 42 138.48889 11.76813 10.25 3 5 8 10 14 17 21 25 98 85 89 73 76 85 87 92 85 56 3 5 8 10 14 17 21 25 20 Descriptive statistics count mean sample variance sample standard deviation minimum maximum range 1st quartile median 3rd quartile interquartile range mode low extremes low outliers high outliers high extremes Value 10 82.60 138.49 11.77 56 98 42 78.25 85.00 88.50 10.25 85.00 0 1 0 0 Normal Probabilities Common Data Mean Standard Deviation 25 4 Probability for a Range From X Value To X Value Z Value for 17 Z Value for 33 P(X<=17) P(X<=33) P(17<=X<=33) 17 33 -2 2 0.0228 0.9772 0.9545 0.02777778 0.33333333 4 24 125 0.0228 0.0456 71292E+013 0.36 49.04 -2.575829 0.001434801