Question

Australia is the first country to make wearing helmets while cycling mandatory. Mandatory Helmet Legislation (MHL) was first introduced in Victoria in July 1990 and the remaining Australian states, Australian Capital Territory and Northern Territory by July 1992. Let μ1 and μ2

​ be the current mean monthly proportion of bicycle-related head injuries in the Australian states and territories of South Australia and Victoria respectively. Data collection were carried out independently in both South Australia and Victoria. First, 29 months were selected at random from January 2018 to December 2022 and the corresponding monthly bicycle-related head injuries (in percentage) were recorded in South Australia. And then, 29 months were selected at random from January 2018 to December 2022 and the corresponding monthly bicycle-related head injuries (in percentage) were recorded in Victoria. The data is stored in the file injury.txt. Assuming proportions of bicycle-related head injuries within each Australian state or territory are independent and identically distributed N(μ1 ,σ² ) and N(μ2 ,σ²
) variables respectively, complete the exercises below. Exercise 1 It is claimed that the mean proportions of bicycle-related head injuries in South Australia and Victoria are different. what is appropriate hypothesis test to use in this situation ? a. one sample t test b. one sample z test c. two sample t test d. paired t test

Answer 1

The appropriate hypothesis test to use in this situation is the two sample t-test. It is used to compare the means of two independent groups.

Step-by-step explanation:

The appropriate hypothesis test to use in this situation is the two sample t-test. This test is used to compare the means of two independent groups to determine if they are statistically different from each other. In this case, we are comparing the mean proportions of bicycle-related head injuries in South Australia and Victoria.

To perform the two sample t-test, we need to calculate the sample means, sample standard deviations, and the sample sizes for both South Australia and Victoria. We can then use these values to calculate the t-statistic and compare it to the critical value to determine if there is enough evidence to reject the null hypothesis.