Question

The Centers for Disease Control and Prevention (CDC) reported that children who have poor oral health often miss more school and receive lower grades. The CDC also reports that 85% of children aged 2 to 17 saw a dentist in the past year. An investigator wants to assess whether use of dental services is similar in children living in the city of Boston. A sample of 125 children aged 2 to 17 living in Boston are surveyed and 64 reported seeing a dentist over the past 12 months. Is there a significant difference in use of dental services between children living in Boston and the national data?

Answer 1

We have given

P0=children aged 2 to 17 saw a dentist in the past year = 0.85

x=64 , n =125

p^=64/125 = 0.512

We want to test Is there a significant difference in use of dental services between children living in Boston and the national data

H0: P=P0=0.85

H1: p not = P0=0.85

Here we have to use z-test

Z_cal= (p^-P0)/sqrt((p^*(1-p^)/n))

=(0.512-0.85)/sqrt(0.512*(1-0.512)/125)

= -7.56

P-value= 0

P-Value < 0.01 hence we reject H0

Yes There is a significant difference in use of dental services between children living in Boston and the national data