Question

19A telecommunications company wants to estimate the proportion of households that would purchase an additional telephone line if it were made available at a substantially reduced installation cost. Data are collected from a random sample of 500 households. The results indicate that 140 of the households would purchase the additional telephone line at a reduced installation cost. Complete parts? (a) and? (b) below.

a. Construct a 95?% confidence interval estimate for the population proportion of households that would purchase the additional telephone line.

b. How would the manager in charge of promotional programs concerning residential customers use the results in? (a)?

Answer 1

a. in this case sample proportion=140/500 =0.28

So, standard error of the sample proportion=(0.28*(1-0.28)/500)^(1/2) =0.02 or 2%

95% confidence interval for this population proportion will be (0.28 -1.96*0.02), (0.28 +1.96*0.02).[at 95% C.I, Z value is 1.96].So, 95% C.I for the population proportion of households that would purchase the additional telephone line will be (0.2408 , 0.3192).

b. For the manager in charge of promotional programs concerning residential customers use the above result in decision making following way:

with 95% probability, it can confirmed that proportion in the whole population have same intention of purchasing the additional telephone line at a reduced installation cost might be 24% to 32%