Probability Values - Degrees of Freedom - Statistics Assignment Help

Assignment Task :

Question 1

We will start with some more practise in looking up tables. State the following probability values – either exact values or the range of possible values indicated on the Statistical Tables. For each part, include a diagram to indicate the area of interest in the relevant distribution. 

(a) P(t > 2.31) (for the t distribution on 18 degrees of freedom) (b) P(t > -1.8727) (for t on 5 df) (c) P(t < -1.7247) (for t on 20 df) (d) P(χ2 > 6.68) (arising from a test of association on a 2x2 contingency table) (e) P(χ2 > 9.50) (arising from a test of association on a 4x3 contingency table) 

Question 2 

This question concerns a study that was introduced in Assignment 2. 

In a study concerning the effectiveness of Ginkgo biloba in treating tinnitus, 24 participants were recruited through advertisements in the national press in the United Kingdom. Once enrolled in the study, participants were asked to complete a number of questionnaires that allowed for the calculation of a severity of tinnitus score. Participants were then instructed to take three tablets a day (each containing 50mg of Ginkgo biloba) over a 12 week period. After this time participants completed the same questionnaires so that their severity of tinnitus could again be calculated. All participants are assumed to have complied with the treatment regimen. 

(a) If the mean severity of tinnitus score for patients at entry to the study was found to be 30.07 units (with a standard deviation of 6.10 units) and after the 12 week period was found to be 27.26 units (with a standard deviation of 5.20 units), using a Type 1 error level of 0.05 (i.e. α = 0.05), determine if there is a “statistically significant” difference in mean score before and after treatment. State the appropriate null and alternative hypotheses, and show all working. 

(b) State and justify your conclusion clearly so that an individual without your statistical knowledge could understand the results. 

Remember to show your working and justify your conclusions. 

Question 3  

This question also concerns a study that was introduced in Assignment 2. 

An article by Holland et al “Does home based medication review keep older people out of hospital?” (British Medical Journal 2005; doi:10.1136) concerned the reporting of evidence obtained through a randomised controlled trial intended to investigate this question. Participants were all patients aged over 80 who had experienced an emergency admission to hospital (for any cause), were prescribed two or more drugs on discharge and were returning to their own home or warden controlled accommodation. 

Participants were randomised to receive either: 

Intervention: two home visits by a pharmacist within two weeks and eight weeks of discharge to 

educate and aid patients with their medications, or Control: standard care. 

Analysis focused on 415 individuals randomised to the intervention and 414 individuals randomised to control. The primary outcome measure was the number of emergency re-admissions to hospital at 6 months. 

The average number of re-admissions was 0.56 (SD = 0.87) for participants randomised to the intervention and 0.43 (SD = 0.73) for participants randomised to control. 

(a) Assuming the number of re-admissions is a continuous variable, test for a difference in (population) average number of re-admissions for participants randomised to the intervention and (population) average number of re-admissions for participants randomised to the control. Use a two-tailed test and assume a Type 1 error level of 0.05 (i.e. α = 0.05) was pre-set as acceptable. Show your working. 

(b) State your conclusion clearly so that an individual without your statistical knowledge could understand the results. 

(c) Without any calculations, briefly explain how the results of a test of a one-tailed alternative hypothesis might differ from those found in (a).

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