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Answer:
a. Best estimate for the mean family size for the population of all families in a country is 16.3571428571
b. 95% confidence interval for the estimate is 16.3571428571±0.7106240840. That is between 15.6465187731 and 17.0677669411
c. The sample is unlikely to be very representative of all families in a country.
Step-by-step explanation:
a. mean family size for the population of all families in a country can be estimated as sample mean, and calculated as:
≈ 16.3571428571
b. 95% confidence interval for the estimate can be calculated using the equation CI=M± where
- M is the mean estimate (16.3571428571)
- t is the corresponding statistic in the 95% confidence level and with 14 degrees of freedom (2.160)
- s is the standard deviation of the sample (1.2309777100)
- N is the sample size (14)
s can be calculated as square root of mean squared differences from the sample mean.
Thus 95% CI=16.3571428571± ≈ 16.3571428571±0.7106240840
The sample is unlikely to be very representative of all families in a country because as the sample data increases, estimate will improve.