1. (25) Suppose that a bag of Skittles contains 20 Reds, 25 Yellows, 22 Purples, 15 Oranges and 18 Greens.

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1 Final Exam Math 11 Name: You will need a calculator for some parts of the exam (TI-83 and TI-84 calculators are available to borrow at the front of the classroom). You should show enough work for me to follow your thought process where possible! Put your answer on the line when provided. 1. (25) Suppose that a bag of Skittles contains 20 Reds, 25 Yellows, 22 Purples, 15 Oranges and 18 Greens. a. In a single random pick, what s the probability to get a Red? b. In a single random pick, what s the probability to get a Red or a Yellow? c. In a sequence of three picks without replacement, what s the probability to get three Reds? d. In a sequence of three picks without replacement, what s the probability to get three of the same color? e. In a sequence of five picks without replacement, what s the probability to get no Reds?

2 2. (25) In an experiment to test for non-celiac gluten sensitivity, 25 subjects who reported gluten sensitivity were placed on a high gluten diet for two weeks, then they were switched to a gluten-free diet for another two weeks. At the end of each two-week period, they were asked to rate their level of digestive distress across several categories, producing a score between 1 and 10 for each person. The table below shows the before and after scores for each of the 25 subjects: Use a 0.05 significance level in a two-tailed test to determine if there is a significant difference in digestive distress on the two diets. a. State the null hypothesis in symbols: b. State the alternative hypothesis in symbols: c. Make a picture of the appropriate sampling distribution, d. Compute the standard deviation of the sampling and accurately label the center and the location of the distribution. sample. e. Compute the test statistic. f. Compute the P-value. g. Draw the appropriate conclusions (both the mathematical statement and the interpretation in context). BONUS: What is the most obvious flaw in the experimental design?

3 3. (25) I currently keep two breeds of chickens Barred Rocks and Australorps. It is easy to tell the eggs apart, because Australorp eggs have a much darker brown shell. In an experiment to test for a significant difference in size, I collected and weighed all the eggs for three days. The data is summarized in the chart below (* indicates a missing data point the Barred Rocks laid more eggs that week). Use a 0.05 significance level in a two tailed-test against the hypothesis that there is no significant difference in the egg size from these two breeds. a. State the null hypothesis in symbols: b. State the alternative hypothesis in symbols: c. Make a picture of the appropriate sampling distribution, d. Compute the standard deviation of the sampling and accurately label the center and the location of the distribution. sample. e. Compute the test statistic. f. Compute the P-value. g. Draw the appropriate conclusions (both the mathematical statement and the interpretation in context).

4 4. (25) In an experiment to test the belief in astrology, 50 subjects were given real readings based on their natal data, and 50 subjects were given false astrological readings obtained by shuffling a set of correct readings. In the group with genuine readings, 46 of the subjects rated their reading as accurate. In the group with false readings, 44 rated their reading as accurate. Use a 0.05 significance level and a one-tailed test to evaluate the claim that the proportion rating a reading as accurate is higher when people receive genuine astrological readings. a. State the null hypothesis in symbols: b. State the alternative hypothesis in symbols: c. Make a picture of the appropriate sampling distribution, d. Compute the standard deviation of the sampling and accurately label the center and the location of the distribution. sample. e. Compute the test statistic. f. Compute the P-value. g. Draw the appropriate conclusions (both the mathematical statement and the interpretation in context).

5 5. (25) In another empirical test of astrology, natal data was taken from a group of 500 nuclear physicists. The distribution of individuals across astrological sign is given below. Since astrological sign is supposedly a good predictor for personality traits such as analytical thinking, ambition and intelligence, we would expect to see a significant deviation from uniformity in the distribution if astrology really worked. Astrological Sign Aries Taurus Gemini Cancer Leo Virgo Libra Scorpio Saggitarius Capricorn Aquarius Pisces Number of Subjects Use a 0.05 significance level to test against the claim that the distribution is uniform. a. What is the expected value for each cell in the table? 2 b. Compute chi-squared ( ). Show all twelve terms in the calculation. c. Compute the P-value. Show what you put in your calculator. d. State your mathematical and contextual conclusions.

6 6. (25) The following data set shows the rate of autism in the United States (children 8 years old, per 1,000) together with the rate of cell phone ownership (percent): x: Cell phone ownership (percent) y: Autism rate (per 1000 children) a. Compute the correlation coefficient for this data. b. Compute the equation of the best fit (regression) line. c. Write down a clear interpretation of the slope of the regression line. d. Use the best fit line to predict the autism rate when cell phone ownership reaches 90%. e. Explain why this data shouldn t convince you that cell phones cause autism.