Question

(4 points) A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 122 people living in Gastown and finds that 21 have an annual income that is below the poverty line. The government official will choose Gastown as a location for one of the social outreach programs if his sample data provide sufficient evidence to support that the true proportion of people living below poverty line is greater than 0.17. A test of hypothesis is conducted. Part i) What is the null hypothesis? A. The true proportion of residents who are living below the poverty line is 0.17 B. The sample proportion of residents who are living below the poverty line is lower than 0.17 C. The true proportion of residents who are living below the poverty line is greater than 0.17. D. The sample proportion of residents who are living below the poverty line is greater than 0.17 E. The sample proportion of residents who are living below the poverty line is 0.17 F. The true proportion of residents who are living below the poverty line is lower than 0.17 Part ii) What is the alternative hypothesis? A. The true proportion of residents who are living below the poverty line is lower than 0.17 B. The sample proportion of residents who are living below the poverty line is lower than 0.17. C. The sample proportion of residents who are living below the poverty line is 0.17 D. The sample proportion of residents who are living below the poverty line is greater than 0.17. E. The true proportion of residents who are living below the poverty line is 0.17 F. The true proportion of residents who are living below the poverty line is greater than 0.17 Part ii) Assuming that 17% of all Gastown residents are living below the poverty line, what model does the sample proportion of residents who are living below the poverty line follow? A. N(0.17, 4.14900) B. Bin(122, 0.17000) C. N(0.17, 0.00308) D. N(0.17, 0.37563) E. N(0.17, 0.03401) Part iv) Assuming that 17% of all Gastown residents are below the poverty line, is the observed proportion based on the 122 sampled residents unusually low, high or neither? A. neither B. unusually low C. unusually high

Answer 1

Solution:

i)ans: F.)

ii.)ans:F.)

iii.)

Standard error 0.17(1 – 0.17) 122 = 0.03401 ans : E.) N(0.17, 0.03401)

iv.)ans: A.)