Business Statistics

Question

How safe are licensed child-care providers? A recent survey by the Consumer Product Safety Commission (CPSC) raised some concerns about possible safety hazards. The CPSC surveyed 220 licensed child-care providers and found that 148 had at least one safety hazard. At 84 of the child-care facilities, children were wearing clothing with neck drawstrings that can possibly cause strangulation, and 42 had cribs with soft bedding that can lead to suffocation.

Set up a 93% confidence interval estimate for the population proportion of licensed child-care providers that have cribs with soft bedding that can lead to suffocation. The lower and upper limits of the confidence interval estimate are:

Lower limit = ?

Upper limit = ?

Answer 1

child-care providers that have cribs with soft bedding that can lead to suffocation, we can use the following formula:

CI = p ± zsqrt((p(1-p))/n)

where:

CI = confidence interval p = sample proportion (42/220 = 0.191) z = z-score for the desired confidence level (0.93/2 + 0.5 = 1.81) n = sample size (220)

Plugging in the values, we get:

CI = 0.191 ± 1.81sqrt((0.191(1-0.191))/220)

Solving for the upper and lower limits of the confidence interval, we get:

Lower limit = 0.105 Upper limit = 0.277

Therefore, we can be 93% confident that the true proportion of licensed child-care providers with cribs containing soft bedding that can lead to suffocation falls between 0.105 and 0.277.