A psychologist claims that the mean age at which children start talking is 12.8 months. Carlos wanted to check if this claim is true. He took a random sample of 20 children and found that the mean age at which these children started talking was 13.9 months with a standard deviation of 1.8 month. Using the 5% significance level, can you conclude that the mean age at which all children will start talking is different from 12.8 months? Assume that the ages at which all children start talking have an approximately normal distribution.
a. How many degrees of freedom will you use for this problem?
b. Find the critical values for this hypothesis test
c. Find the test statistic to.
d. Find the p-value for this test
e. Use the p-value to draw a conclusion.
f. Find the 95% confidence interval for the mean age at which all children start talking.
g. Use the confidence interval to test whether the mean age at which children start talking is 12.8 months.