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# Statistics in the Courtroom

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Explain why figure 1 suggests Ms. Gilbert is guilty of excess deaths on the ward.
Explain why figure 1 is not conclusive evidence of Ms. Gilbert’s guilt.
What is the relevance of the coin-tossing story to the trial?
Cobb argued that a jury would likely fall into the “prosecutor’s fallacy”. What is the “prosecutor’s fallacy” and why is the defense concerned about it?

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Formula SheetPreview the document

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1. (5 points) A solar company claims its customer will save an average of \$80 per month. A consumer protection agency feels that this claim is too high. If they randomly selected a sample of 36 customers and the mean savings was found to be \$73 with a standard deviation of \$16.70, perform a hypothesis test at the 5% significance level to determine if the actual savings is less than the company claims.

a. State the null and alternative hypothesis
b. Find the critical value(s) for the 5% significance level
c. Compute the test statistic
d. Compute the p-value
e. What do you conclude from your hypothesis test?

2. (5 points) The DMV reports that 5.6% of adult drivers will get into an accident in the next year. A researcher wants to know if the proportion of teenage drivers who get into an accident is different. She surveys 10,000 teenage drivers and finds that 614 got into an accident in the last year. Determine if the percentage of accidents is different for 16-year-old drivers than adults at the 5% significance level. Show all work.

a. Null and Alternative Hypothesis
b. Test Statistic
c. Critical Value(s)
d. P-value
e. State the final conclusion that addresses the original claim

3. (5 points) In a study by Stephens, Atkins, & Kingston (2009) each participant was asked to plunge a hand into icy water and keep it there as long as the pain would allow. In one condition, the participants repeated their favorite curse words while their hands were in the water. In the other condition the participants repeated a neutral word. Data similar to the results obtained in the study are shown in the following table. Do these data indicate a significant difference in pain tolerance between the two conditions? Use a two-tailed test with α = .05.

a. Null and Alternative Hypothesis
b. Test Statistic
c. Critical Value(s)
d. P-value
e. State the final conclusion that addresses the original claim

Amount of Time (Seconds)

Participant

Swear Words

Neutral Words

1

94

59

2

70

61

3

52

47

4

83

60

5

46

35

6

117

92

7

69

53

8

39

30

9

51

56

10

73

61

4. (5 points) A study was done about how often different age groups use their phones. When 258 people in the age group 20-39 were surveyed, 69% brought their phones to bed with them. When 129 people in the age group 40-49 were asked the same question, 52% answered “yes”. Perform a hypothesis test at the 5% significance level to determine if there is a difference between proportions.

a. Null and Alternative Hypothesis
b. Test Statistic
c. Critical Value(s)
d. P-value
e. State the final conclusion that addresses the original claim

Last Updated on March 9, 2018

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