Where appropriate, use the 5-step procedure. Please paste all relevant output.

1. Automobile insurance is much more expensive for teenage drivers than for older drivers. To justify this difference, insurance companies claim that teenage drivers are much more likely to be involved in costly accidents. To test this claim, a researcher obtains information about registered drivers from the department of motor vehicles and selects a sample of n = 300 accident reports from the police department. The breakdown of accident reports was as follows

   Under 20	20-29	30 or older
   25%	32%	43%

   
   Test the hypothesis that there is no difference between age groups. (25)
2. A study was done on students convicted of underage consumption at Tiffin University. The researchers looked at the gender of the student and the location where they were arrested for their underage violation. Using the data found in the SPSS data file, "Underage," test at a .05 level of significance, whether there is a relationship between gender and location. (25)
   Solution: We need to test:
   \[\begin{aligned}
   & {{H}_{0}}:\text{ Gender and location are not related} \\
   & {{H}_{A}}:\text{ Gender and location are related} \\
   \end{aligned}\]
   Using SPSS, we get the following crosstab:

   Gender * Location Crosstabulation
   Count
   		Location			Total
   		Dorm	Bar	Other Location
   Gender	female	5	2	16	23
   	male	3	5	17	25
   Total		8	7	33	48

   
   Now, we get the following statistics from SPSS:

   Chi-Square Tests
   	Value	df	Asymp. Sig. (2-sided)
   Pearson Chi-Square	1.736 a	2	.420
   Likelihood Ratio	1.781	2	.411
   Linear-by-Linear Association	.134	1	.714
   N of Valid Cases	48
   4 cells (66.7%) have expected count less than 5. The minimum expected count is 3.35.

   Directional Measures
   			Value	Asymp. Std. Error a	Approx. T b	Approx. Sig.
   Nominal by Nominal	Lambda	Symmetric	.053	.072	.711	.477
   		Gender Dependent	.087	.118	.711	.477
   		Location Dependent	.000	.000	. c	. c
   	Goodman and Kruskal tau	Gender Dependent	.036	.051		.428 d
   		Location Dependent	.012	.017		.576 d
   Not assuming the null hypothesis.
   b. Using the asymptotic standard error assuming the null hypothesis.
   c. Cannot be computed because the asymptotic standard error equals zero.
   d. Based on chi-square approximation

   
   The table above shows that the assumptions for the Chi-Square test are not met (there are too many cells with a expected count less than 5). We use instead Lambda. We find that \(\lambda =0.53\), and the corresponding p-value is p = 0.477 > 0.05, which means that we fail to reject the null hypothesis.
   This means that the sample data doesn’t provide enough evidence to claim that gender and location are related.
   For the following, please give the appropriate statistical test and the reasoning for choosing it.
3. Prosecutors in sexual assault cases are often hampered by stereotypical notions that jurors have about rape. A researcher administered a rape myth scale to a group of subjects and then had them read a scenario depicting a rape case. In the case, a female is out at a bar and meets a guy. They have a nice conversation and at the end of the evening, she agrees to give this man her phone number. Unbeknownst to her, the man follows her home, breaks into her house and rapes her. Subjects were then asked to rate on a scale of 1 to 10, whether they agreed that a rape had occurred in this scenario. The higher the score, the more likely it was that the subject believed that the female in the scenario was raped. The researcher analyzed the scores of the rape myth scale and organized the subjects into two groups: high rape myth and low rape myth. Test the hypothesis that the high rape myth group will be less likely to agree that a rape occurred in the scenario compared to the low rape myth group. (10)
4. A large, multi-state law enforcement operation crackdown on people who chronically fail to pay child support revealed that the average (mean) amount owed by these people was $75, 200. A sample of 14 "deadbeat dads" is taken from the State of Ohio. The mean delinquent amount from that sample was $72,500 with a standard deviation of $3900. Test the hypothesis that Ohio deadbeats are no different from the national sample. (10)

1. The U.S. prison population grew exponentially between 1980 and 2000. A researcher is interested in testing to see whether that increase reflected increases in crime or whether it was the result of a conservative shift that occurred during this same time. Crime data was collected for the decades of the 70s, 80s and 90s. The researcher wants to test the hypothesis that there was no difference in the number of UCR Part 1 crimes during those 3 decades. (10)
2. O.J. Simpson has become the great American tragedy. During his trial, public opinion about his guilt or innocence varied along both gender and racial lines. A study was done to test a hypothesis that there would be differences in whether people would vote guilty or not guilty depending on if they were male or female and if they were Black or White. (10)
3. A study was done to test for the effect of vividness of evidence presented on damage awards in a civil trial. Subjects were presented with the facts of a case in which a woman drove over a manhole cover while exiting a bank parking lot. The cover became dislodged and struck the underside of the vehicle. The impact ruptured the gas tank of the vehicle and it burst into flames killing the driver. Subjects read one of 3 versions of the case: text only, text with color photos of the burned out vehicle or text with computer animation of the accident, and were asked to give a dollar amount that they thought the victim’s spouse should receive in damages. The hypothesis that method of presentation would affect the amount of money awarded for damages was tested. (10)
4. Sometimes, it takes multiple statistical tests to figure out what you want to know. The SPSS data file ‘Yates’ contains some data from a research project based on the Andrea Yates case. The researcher was interested in whether or not parents would be more punitive towards Yates, who murdered her five children but was ultimately found NGRI by a jury. Subjects who were either parents or non-parents read a summary of a case based off the Yates case and were asked to select a sentence option from the following choices:

__________ no punishment

__________ probation with no time spent in prison

__________ confinement in a mental hospital

__________ 1 year in a county jail

__________ 5 years in a state prison

__________ 10 years in a state prison

__________ life in prison with the possibility of parole after 25 years

__________ life in prison with no possibility of parole

__________ the death penalty

1. Treat the sentence data as interval and conduct a t-test to test a hypothesis that there will be no difference between parents and non-parents in sentence (do not use the 5-step procedure, simply conduct the test and decide whether or not to reject the null hypothesis) (5)
2. Upon further consideration, the researcher is concerned that perhaps this data is ordinal. Perform a chi-square test to see if there is a difference in sentence based on parental status (do not use the 5-step procedure, simply conduct the test and decide whether or not to reject the null hypothesis) (5)
3. Finally, what the researcher is most interested in is whether or not parents will be more likely to vote for the death penalty than non-parents. Using the results from (b), test for a difference in death sentences between parents and non-parents (do not use the 5-step procedure, simply conduct the test and decide whether or not to reject the null hypothesis) (5)

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