Statistics Questions Coursework Example

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Statistics Questions
Statistics in the Courtroom
Reason Figure 1 Suggests Ms Gilbert Is Guilty Of Excess Deaths on the Ward
Figure 1 showed that between 1990 and 1995, there is one shift with 25 to 35 deaths per year. In 1990, Ms Gilbert started work at the medical ward and halted work at the VA in 1996. It showed fewer deaths when she was not working at the VA, and very many deaths during the period she was present. From 1991 to 1995, the evening shift had very many deaths, and during that period Ms Gilbert was assigned to the evening shift. In 1990, she was working the night shift that experienced exceptionally high mortality. Consequently. Figure 1 Suggests Ms Gilbert Is Guilty Of Excess Deaths on the Ward.
Reason Figure 1 Is Not Conclusive Evidence of Ms Gilbert’s Guilt
The pattern shown in Figure 1 could have been due to typical, expected factors thus the prosecution introduced a statistical test.
The relevance of the Coin-Tossing Story to the Trial
The coin-tossing story was used to explain the use of p-value to identify the likelihood of chance-like variation.
Prosecutor’s Fallacy
The Prosecutor’s Fallacy refers to the incorrect interpretation of a correct statistic (Bolton 52). The defence is concerned about it because it encourages false logic that could be used as the basis for arguments thus leading to misinterpretation by the jury and the incrimination of Ms Gilbert.
Solar Company Claim
Null and Alternative Hypothesis
The null hypothesis is: “The consumer protection agency claim that the actual savings are on average $80 per month”.

The alternative hypothesis: “The consumer protection agency claim that the actual savings are on average less than $80 per month”.
Critical Value
α=0.051-0.05=0.45After looking up .975 on the Z-score chart, Z was determined to be 1.645
Critical Value (Z-score) = 1.645
Test Statistic
t=x-u0s/√nt=73-8016.7/√36t=-716.7/6t=-72.783t=-2.515P-Value
Degree of freedom=n-1=36-1=35Using symmetry rule,
t=2.515From t-table,
0.05<p<0.1Conclusion
The p-value is between .05 and 0.1 which is greater than .05. Thus, we can conclude that there is no statistically significant difference between the average savings claimed by the consumer protection agency and the average savings from the samples. Consequently, we accept the null hypothesis and conclude that the consumer protection’s claim is correct.
DMV Report
Null and Alternative Hypothesis
The null hypothesis is: “There is no significant difference in the percentage of accidents between 16-year-old drivers and adults”. The alternative hypothesis: “There is a substantial difference in the percentage of accidents between 16-year-old drivers and adults”.
Test Statistic
p=61410000=0.0614Z= p-p0p0(1-p0)nZ= 0.0614-0.0560.056(1-0.056)10000Z= 0.00540.056(1-0.056)10000=0.00540.002299Z= 2.349Critical Value(s)
α=0.051-0.05=0.45After looking up .45 on the Z-score chart, Z was determined to be 1.645
Critical Value (Z-score) = 1.645
P-value
Z=2.349From z-table,
p=.0096Conclusion
The p-value is between .0096 which is less than .05. Therefore, we can resolve that there is a statistically significant difference in the percentage of accidents between 16-year-old drivers and adults. Thus, we reject the null hypothesis and conclude that there is no difference percentage of accidents between 16-year olds and adults.
Pain Tolerance
Null and Alternative Hypothesis
The null hypothesis is: “There is no significant difference in pain tolerance when the participants repeated their favourite curse words and when the participants repeated a neutral word”. The alternative hypothesis: “There is a substantial difference in pain tolerance between the participants who repeated their favourite curse words and the participants who repeated a neutral word”.
Test Statistic
x=∑xnx1=94+70+52+83+46+117+69+39+51+7310 And x2=59+61+47+60+35+92+53+30+56+6110×1=69.4 And x2=55.4s=1Ni=1N(xi-x̄)2s1=(94-69.4)2+(70-69.4)2+(52-69.4)2+(83-69.4)2+(46-69.4)2+(117-69.4)2+(69-69.4)2+(39-69.4)2+(51-69.4)2+(73-69.4)210-1
s1=605.16+0.36+302.76+184.96+547.56+2265.76+0.16+924.16+338.56+12.9610s1=5182.410= 22.765s2=(59-55.4)2+(61-55.4)2+(47-55.4)2+(60-55.4)2+(35-55.4)2+(92-55.4)2+(53-55.4)2+(30-55.4)2+(56-55.4)2+(61-55.4)210s2=12.96+31.36+70.56+21.16+416.16+1339.56+5.76+645.16+0.36+31.3610sz=2574.410= 16.045n1=10, x1=69.4, s1=22.765n2=10,×2=55.4,s2=16.045t=x̄1-x2-Δs12n1+s22n1 t=69.4-55.4-022.765210+16.045210 t=14518.24+257.44 t=1427.851 t=0.503Critical Value(s)
α=0.051-0.05=0.45After looking up .45 on the Z-score chart, Z was determined to be 1.645
Critical Value (Z-score) = 1.645
P-value
Degree of freedom=n-1=36-1=35t=0.503xc2=(OI-EI)2EIxc2=(94-59)259+(70-61)261+(52-47)247+(83-60)260+(46-35)235+(117-92)292+(69-53)253+(39-30)230+(51-56)256+(73-61)261xc2=20.763+1.328+0.532+8.817+3.457+6.793+4.830+2.7+0.446+2.361xc2=52.027From chi-square distribution table,
0.025<p<0.05Conclusion
The p-value is between .025 and .05 which is less than .05. Therefore, the overall deduction is that there is a statistically substantial variations in pain tolerance between the participants when they repeated their favourite curse words and the participants when they repeated a neutral word. Thus, we accept the alternative hypothesis and resolve that the two conditions resulted in a difference in pain tolerance for the participants.
Phone Use
Null and Alternative Hypothesis
The null hypothesis is: “There is no substantial difference in phone use among the people in the 20-39 age group and people in the 40-49 age group”. The alternative hypothesis: “There is a significant difference in phone use between the people in the 20-39 age group and people in the 40-49 age group”.
Test Statistic
n1=258,p1= 69%=0.69, y1=0.69*258=178n2=129 ,p2= 52%=0.52, y1=0.52*129=67Z=p1-p2p(1-p)(1n1+1n2)Where:
p=y1-y2n1+n2p=178+67258+129= 245385=0.6363Therefore,
Z=0.69-0.520.3636(0.6363)(1258+1129)Z=0.170.23130.0116=0.170.0518=3.282Critical Value(s)
α=0.051-0.05=0.45On checking .45 on the Z-score table, the critical value was seen to be 1.645
Critical Value (Z-score) = 1.645
P-value
Z=3.282From z-table,
p=.9995Conclusion
The p-value is between .9995 which is more than .05. Therefore, the overall deduction is that there is no statistically substantial difference in phone use between the people in the 20-39 age group and people in the 40-49 age group. Consequently, we accept the null hypothesis and conclude that there is no variations between proportions.

Work Cited
Bolton, Derek. “The prosecutor’s fallacy at work.” NEW SCIENTIST 231.3089 (2016): 52-52.