SIT191 - Problem Solving Task - The Xtreme and the Firebird - Statistics Assignment Help

Assignment Task

1. A catheter is a small tube that can be used in an angiogram. It is threaded into the heart from a vein in the patient’s leg to help examine heart problems. It is important that the company that manufactures the catheters maintains a diameter of 2.00 mm.
A random sample of 10 catheters is taken and the diameters (in mm) given below.
1.93 1.94 1.95 2.03 1.92 2.04 1.98 2.01 2.02 1.93
a) Create a 95% confidence interval for the mean diameter of catheters produced by the company.
b) Interpret your interval in the context of the question.
c) Perform a hypothesis test to find out if the mean diameter of the catheters is significantly different to the required 2.00 mm. Use α=0.05.
d) Are the assumptions required for the test you performed met? Discuss briefly.

2. Two model helicopters, the Xtreme and the Firebird, were tested through an obstacle course. Twelve volunteers flew each model through the same obstacle course. The time taken (in seconds) by the models to complete the course was recorded for each volunteer and given below. The order in which the models were flown was randomised for each volunteer.
Flight Time (secs)
Volunteer: 1 2 3 4 5 6 7 8 9 10 11 12
Xtreme 30 32 18 19 27 26 26 30 21 29 20 30
Firebird 25 28 20 14 22 23 22 34 19 30 16 29
a) Explain why:
i) the times should be analysed as paired data.
ii) it was important to randomise the order in which the models were flown for each volunteer.
b) Is the Firebird significantly faster through the obstacle course than the Xtreme? Carry out a hypothesis test using α = 0.025.
c) Calculate a 95% confidence interval for the difference in time for the two helicopter models and interpret the interval.
Based on your hypothesis test result, did you expect to find 0 in the interval? Explain.

3. The amount of calcium in the blood was compared for men and women of the same age.
Researchers measured the serum calcium (mmol/l) for 91 men and 84 women.
The data are summarised below.
              Mean     Std. Dev.
Men       2.318       0.122
Women 2.397        0.137
a) Do men and women of this age have significantly different serum calcium levels?
Carry out a hypothesis test with a significance level of 5%.
b) Create a 95% confidence interval for the mean difference in serum calcium, and interpret the interval.
c) Is the confidence interval consistent with your conclusion from a)? Explain.
d) Is it necessary for the test you used that serum calcium is normally distributed? Explain

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