The 90% confidence interval for the proportion of Los Angeles residents with a landline telephone, based on a sample of 200 individuals with 96 having a landline, is approximately 42.8% to 53.2%.
The subject of this question is Mathematics, specifically in the field of statistics where constructing confidence intervals is a common practice.
The question asks for the calculation of a 90% confidence interval for the proportion of Los Angeles residents who have a landline telephone, given that 96 out of 200 randomly selected residents have a landline.
To calculate the confidence interval, we'll use the sample proportion (p-hat) which is 96/200 = 0.48, and the formula for a confidence interval for a proportion which is:
p-hat ± z*(√(p-hat(1-p-hat)/n))
For a 90% confidence level, the z-value (z*) is about 1.645.
Thus, the calculation for the confidence interval is:
0.48 ± 1.645*√(0.48(1-0.48)/200)
This results in an interval approximately from 0.428 to 0.532.
Therefore, the market analyst can be 90 percent confident that the true proportion of LA residents with landline phones lies between 42.8% and 53.2%.