# The binomial test

The binomial test

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PART 1: The binomial test

2. Insurance companies charge young drivers more for automobile insurance because they tend to have more accidents than older drivers. To make this point an insurance representative first determines that only 16% of licensed drivers are age 20 or younger. Because this age group makes up only 16% of the drivers it is reasonable to predict that they should be involved in only 16% of the accidents. In a random sample of 100 accident reports however the representative finds 31 accidents that involved drivers who were 20 or younger. Is this sample sufficient to show that younger drivers have significantly more accidents then would be expected from the percentage of young drivers? Use a two-tailed test with a significance of .05

4. During the 2004 Olympic Games, Hill and Barton monitored contests in four combat sports: Greco-Roman wrestling, freestyle wrestling, boxing, and tae kwon do. Half of the competitors were assigned red outfits and half were assigned blue. The results indicate that participants wearing red won significantly more contests. Suppose that a sample of n=100 contests produced 60 winners wearing red and only 40 wearing blue.

A. is this enough evidence to justify a conclusion that wearing red produces significantly more wins than would be expected by chance? Used a two tailed test with a significance of .05

B. Because the outcome of the binomial test is a borderline z-score use the real limits for X=60 to determine if the entire z-score interval is located in the critical region. If any part of the interval is not in the critical region the correct decision is to fail to reject the null hypothesis.

6. A researcher would like to determine whether people really can tell the difference between bottled water and tap water. Participants are asked to taste two unlabeled glasses of water one bottled and one tap and identify the one they thought tasted better. Out of 40 people in the sample 28 picked the bottled water. Was the bottled water selected significantly more often than would be expected by chance? Use a two tailed test with a significance of .05

<pclass=”msonormal” style=”font-family: Verdana, arial, sans-serif; line-height: normal;”>24. A researcher is testing the effectiveness of a skills mastery imagery program for soccer players. A sample of n=25

college variety players is selected and each player is tested on a ball handling obstacle cause before beginning the imagery program and again after completing the 5-week program. Of the 25 players 18 showed improvement performance on the obstacle courses after the imagery program and 7 were worse.

A. is these results sufficient to conclude that there is a significant change in performance following the imagery program use a two tailed test .05

<pclass=”msonormal” style=”font-family: Verdana, arial, sans-serif; line-height: normal;”>

26. Trying to fight drug resistant bacteria a researcher tries an experimental drug on infected subjects. Out of 70 monkeys 42 showed improvements 22 got worse and 6 showed no change. Is this researcher working in the right direction? Is there a significant effect of the drug on the infection? Use two tailed test at .05

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