Assignment Task
1 PRP (platelet rich plasma) therapy is used to treat chronic joint pain and tendon injuries, using plasma derived from the blood of a patient. A study involving 245 patients with lateral epicondylar tendinopathy (tennis elbow) reported that after receiving a PRP injection, 210 patients experienced at least a 25% reduction in pain.
Is there evidence that the PRP treatment relieves pain in more than 80% of patients with tennis elbow?
a) Write appropriate hypotheses.
b) Check the assumptions and conditions.
c) Perform the hypothesis test and find the P-value.
d) State your conclusion in plain English. Use a significance level of 5%.
e) Give a 90% confidence interval for the true proportion of patients with tennis elbow whose pain is reduced by PRP therapy, and interpret your interval.
f) Comment on your confidence interval in relation to your conclusion from part d).
2 Phenylthiocarbamide (PTC) is a compound that has a strong bitter taste for some people and is tasteless for others. The ability to taste this compound is an inherited trait. A study found that 558 out of 790 Irish people could taste the compound, while 412 of 550 Italian people could taste it.
Is there evidence that the proportion of Italian people who can taste PTC is significantly different to the proportion of Irish people who can taste PTC?
a) Write appropriate hypotheses.
b) Perform the hypothesis test, find the P-value and state your conclusion in plain English. Use α = 0.02.
c) Create a 98% confidence interval for the difference in the proportions of PTC tasters, and interpret your interval.
d) Explain how your interval is consistent with your conclusion from b).
3. A report on fatal car accidents found that 19% of the accidents involved alcohol, 32% involved speeding and 12% involved alcohol and speed. Let A be the event that alcohol was involved in the fatal accident, and let B be the event that speed was involved. Using a Venn diagram or otherwise, answer the following.
a) What is the probability that a fatal accident didn’t involve speed or alcohol?
b) P(A and B)
c) P(A or B)
d) P(A|B)
e) Are the involvement of speed and alcohol in fatal accidents mutually exclusive events? Explain.
f) Are speed and alcohol in fatal accidents independent events? Explain.
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4. Barramundi is a fish species found in the Northern Territory and the north of Western Australia and Queensland. At one location, the average length of adult barramundi is 93.5 cm, with standard deviation 14 cm. Assume barramundi length is normally distributed.
a) Use the 68-95-99.7% rule to find the percentage of adult barramundi expected to be between 79.5cm and 121.5cm.
b) What proportion of the adult barramundi at the location are
i) at least 110 cm?
ii) between 75 cm and 95 cm?
c) What is the cut off length for the longest 15% of barramundi?
d) Give the inter-quartile range of the barramundi.
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