Question

update I have finished 1-5 6-9 are stumping me

"Durham Police is to become the first force in the country (UK) to introduce a scheme in which users are treated with diamorphine - medical grade heroin.
Ron Hogg, County Durham's Police, Crime and Victims' Commissioner, says such treatment lowers offending levels.
Opponents claim trials have not shown significant benefits.
Mr Hogg told BBC Newcastle existing national policies had not been effective and pointed to six-year trials in Darlington, London and Brighton which he said had helped wean users off the drug.
Addicts were given the opiate in consumption rooms, often referred to as "shooting galleries", supervised by medical professionals.
"It got them back into a normal life and it cut crime," he said.
"We saw health benefits for the individuals, we saw needles being taken off the street, so there's an awful lot of evidence both in the UK and across the world that such schemes do actually work.
"All police and crime commissioners spend a lot of money on what we call diversionary work - community projects and youth offending schemes - because we know this will stop people committing crime.
"This is just an extension of that rationale. The controversiality is because it's drugs."
'Not unusual'
Mr Hogg said the UK had the highest rate of heroin, cocaine and ecstasy use across the European Union with drug-induced deaths totalling 45 people per million compared with 17 per million in the EU.
Aiming to introduce the scheme "by the end of this year", he added the force's public health partners were working out the cost of administering the drug to users twice-daily.
He previously mooted such a move in 2013.

"If we go back to the 1960s, doctors used to prescribe heroin as a means of treating someone back to recovery. It's not that unusual," he said.
"We've got to consider the Misuse of Drugs Act has been in since 1971 and we haven't arrested the way out of the problem, have we?"
A Home Office spokesman said there was evidence "supervised use of [diamorphine] in a medical environment as part of a treatment plan can help keep patients in treatment and out of criminal behaviour".
However, David Raynes of the National Drug Prevention Alliance, warned the move "will not stop addicts being addicts".
"It doesn't stop people using street drugs," he said.
"It may reduce crime marginally, but it doesn't reduce crime permanently."

Working together as a group, design a study to address whether this method is effective or not in reducing crime due to heroin addiction. Ron Hogg of County Durham's Police believes it works while David Raynes of the National Drug Prevention Alliance is skeptical. Your job is to help settle the argument using a statistical study. You will need to address the following in your write up:

1 What is the population of interest?

2 What are the null and alternate hypotheses of your study?

3 What data type will you be collecting in this study (numerical or categorical)?

4 How would you collect the data needed to decide which hypothesis to support?

5 How would you make sure the data collected is representative of the population of interest and not biased?

6 Specifically, what tools would you use to analyze the data? You need to give the names of any plots/graphs that would be useful and the type of hypothesis test that would be used to settle the argument between Mr. Hogg and Mr. Raynes.

7 Based on what hypothesis test you selected in part 6, what assumptions need to be check prior to using said test?

8 Let's assume your study resulted in the data being statistically significant. Which hypotheses would have been supported? Give a possible p-value for this result. If an error had occurred, which type (Type I or Type II) could it have been?

9 Let's assume your study resulted in the data NOT being statistically significant. Which hypotheses would have been supported? Give a possible p -value for this result. If an error had occurred, which type (Type I or Type II) could it have been?

Answer 1

1.

Population of interest is - all the heroin drug addicts in UK who are committing crimes.

5.

BY collecting the sample(or samples) of sufficient size by following appropriate sampling techniques such as stratified random sampling to cover all the homogeneous areas/provices/states with considerable crime rates due to heroin addicts.

6.

Scatter plots would be used to analyze the data(crime rates on Y-axis and previous time periods to present time periods on X-axis for control group and treatment groups: separate scatter plots or the same with different colored lines) and ANOVA test followed by post - hoc test(if significant difference exists as per ANOVA) would be used. (if only one treatment group is used with a control group, Independent samples t-test would be sufficient) (if the same criminals' crime rates for previous time periods and for present time periods are compared, then Dependent samples t-test would be sufficient). Previous periods means before treatment and present periods means after treatment.

9.

Null Hypothesis(H0) would have been supported because no statistical significance is the result of failing to reject null hypothesis.

We fail to reject the null hypothesis if p-value is greater than the significance level (alpha). Thus, if alpha is 0.05 (which is mostly used), the possible p-value for the result would be any value greater than 0.05 and p-value lies between 0 and 1, thus possible p-values would be 0.06 or 0.07 or 0.08 or 0.09 or 0.90 or 0.055, etc,.

If an error had occurred, it could have been a type II error because a type II error is failing to reject a false null hypothesis.