Exam 1A: Chapters 9, 10, 7.3, & 15.3
Preisler
2. In a random sample of 77 children, the mean age at which they first began to combine words was 16.51 months, with a standard deviation of 9.59 months.
a. Check the validity of the confidence interval. (5 pts.)
n=77
ar{x} =16.51
SD=9.59
The variable is age at which children combine words and is normally distributed.
The problem states a random sample of 77 children was taken.
The population distribution is unknown. The sample size of 77 is large enough so that the central limit theorem applies and the sampling distribution will approximate a normal distribution.
b. Construct a 95% confidence interval for the true mean age at which children first begin to combine words. (5 pts.)
c. Interpret the confidence interval. (5 pts.)
We are 95% confident that the true mean age at which children first begin to combine words falls within 14.33 to 18.69 months.
d. Would 13.5 months be a plausible value for the population average? Explain why & Justify. (3 pts.)
No, 13.5 months would not be a plausible value for the population average because it falls outside the 95% confidence interval of 14.33 to 18.69 months. This suggests that there is only a 5% chance that the true population mean is less than 14.33 months.