# Question 3 Data source: Land Transport Safety Authority (a) In a survey conducted in 2004, 52...

Question 3 Data source: Land Transport Safety Authority (a) In a survey conducted in 2004, 52 cyclists in Northland were observed wearing helmets while an additional 9 were observed without helmets. The national proportion of cyclists who wear helmets was estimated to be 92%.

(i) Check the requirements for the normal approximation in this case and explain what this suggests about conducting a hypothesis test of H0: p = 0.92 using this sample.

(ii) Calculate a 95% confidence interval for the proportion of helmet?wearing cyclists in Northland (check the requirements first).

(iii) Doesthe confidence interval indicate that the proportion in Northland issignificantly different from the estimated national proportion? Explain in one or two sentences. In a similar survey in 2004 conducted on the West Coast of the South Island, 115 out of 121 cyclists were observed wearing helmets.

(iv) Test, using ? = 0.05, using this sample whether the proportion of cyclists who wear helmets on the West Coast is the same as nationally (i.e. 92%) with H0: p = 0.92. Check the requirements for this test and comment on the validity of the test.

(v) Calculate a 95% confidence interval for proportion of cyclists wearing helmets on the West Coast of the South Island and write a sentence to compare it with the interval found in part (ii) (check the requirements first).

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