A researcher read that firearm-related deaths for people aged 1 to 18 were distributed as follows:
74% accidental, 16% homicides, 10% suicides. In her district, there were 34 accidental deaths, 13 homicides and 3 suicides during the past year. Perform a chi-square goodness-of-fit test to test if the distribution of firearm-related deaths in the researcher’s district are comparable to the distribution given. You are given the actual numbers of firearm-related deaths for the researcher’s district. Under the assumed distribution, how many would you expect to see in each of the three categories? Please show your work.

a. The expected number of accidental deaths in the researcher’s district is:

b. The expected number of homicides in the researcher’s district is:

c. The expected number of suicides in the researcher’s district is:

d. The chi-square test statistic is ______. Round to two digits beyond the decimal.

e. At the 0.05 significance level, the critical value is: