Answers to Selected Problems
Answers to Selected Problems
Dental services problem - Bottom of Page 5
The NCHS report indicated that in 2002, 75% 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?
- Step 1: Set up hypotheses and determine the level of significance.
α=0.05
- Step 2: Select the appropriate test statistic.
First, determine whether the sample size is adequate.
Therefore the sample size is adequate, and we can use the following formula:
- Step 3: Set up the decision rule.
Reject H0 if Z is less than or equal to -1.96 or if Z is greater than or equal to 1.96.
- Step 4: Compute the test statistic
- Step 5: Conclusion.
We reject the null hypothesis because -6.15<-1.96. Therefore there is a statistically significant difference in the proportion of children in Boston using dental services compated to the national proportion.