Question

A city councilor asks your advice on how many householders should be polled in order to gauge the support for a tax increase to build more schools. Suppose you conduct the survey and construct a confidence interval for the true proportion of householders who are in favor of the tax increase to be (0.345, 0.452). Which of the statement(s) below is (are) a correct interpretation of the confidence interval? Check all that apply.

I) There is a 95% chance that 39.85% of householders are in favor of the tax increase.

II) It is reasonable to conclude that fewer than 50% of the householders are in favor of the tax increase.

III) If we were to use the collected data to test the hypotheses, H0: p=0.30 versus HA: p>0.30 we would reject the null hypothesis if α=0.05

IV) We can be 95% confident that the true proportion of householders who are in favor of the tax increase is contained in the interval we constructed.

Answer 1

The correct interpretation for 95% confidence interval is,

IV) We can be 95% confident that the true proportion of householders who are in favor of the tax increase is contained in the interval we constructed.

( Because the first option not correct because it represent the probability, 2nd option is not correct because it tells about 50% chances but we don't have evidence The 3rd option is decision rule so it is also not a interpretation. And fourth one is interpretation. Therefore 1st and 4th is option)

(Hope this help you Thank you.)