Answer:
(0.407,0.471)
Explanation:
To find the 95% confidence interval for the true proportion, we can use the following formula:
CI = p ± zsqrt((p(1-p))/n)
where:
p = sample proportion = 442/1004 = 0.4392
n = sample size = 1004
z = z-score corresponding to the desired confidence level (95% = 1.96)
Substituting the values, we get:
CI = 0.4392 ± 1.96sqrt((0.4392(1-0.4392))/1004)
CI = 0.4392 ± 0.032
Therefore, the 95% confidence interval for the true proportion of people who feel that keeping a pet is too much work is (0.407, 0.471).