Full moon Some people believe that a full moon elicitsunusual behavior in people. The table shows the numberof arrests made in a small town during weeks of six fullmoons and six other randomly selected weeks in thesame year. We wonder if there is evidence of a differencein the types of illegal activity that take place.a) Will you test goodness-of-fit, homogeneity, orindependence?b) Write appropriate null hypotheses.c) Find the expected counts for each cell, and explainwhy the chi-square procedures are not appropriate. Full Moon Not FullViolent (murder, assault, rape, etc.) 2 3Property (burglary, vandalism, etc.) 17 21Drugs/Alcohol 27 19Domestic Abuse 11 14Other Offenses 9 6

ific Calculator Of30shg/ckivdfk1p00003g5tgeftOid1 Agroup of researchers in New York wants to test if there is any relationship between living in California and preferring warm weather to cold weather. The researchers send out an online questionnaire to 200 randomly chosen people in the US asking several questions including: "Do you live in California?" and "Do you prefer warm weather to cold weather?". The results are summarized in the table below: Prefers Warm Weather 80 Prefers Cold Weather 42 Lives in California Doesn't Live in California 35 43 Test the null hypothesis that the choices on these two questions are independent versus the alternative that they are dependent. What are the p-value and conclusion of this test if the test is performed at the alpha =0.1 level? %3D p-value = 0.0091; Fail to reject the null hypothesis %3D p-value = 0.0039; Reject the null hypothesis p-value = 0.0039; Fail to reject the null hypothesis p-value = 0.0911; Reject the null hypothesis NEXT

Define the following with an example  (a) random experiment      (b) sample space (c) events (d) independent events

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Bernoulli 2 Do these situations involve Bernoulli trials?Explain.a) You are rolling 5 dice and need to get at least two 6’sto win the game.b) We record the distribution of eye colors found in agroup of 500 people.c) A manufacturer recalls a doll because about 3% havebuttons that are not properly attached. Customersreturn 37 of these dolls to the local toy store. Is themanufacturer likely to find any dangerous buttons?d) A city council of 11 Republicans and 8 Democrats picks a committee of 4 at random. What’s the prob-ability they choose all Democrats? e) A 2002 Rutgers University study found that 74% ofhigh school students have cheated on a test at leastonce. Your local high school principal conducts asurvey in homerooms and gets responses that admitto cheating from 322 of the 481 students.