Television programs geared toward children can be beneficial to their learning, but too much television watching has been shown to be detrimental. In 2000, it was stated that the average number of television hours watched per week by a child between 2 and 5 years old was 27 hours. A study in 2010 aimed to test if this number increased. A total of 100 households with a children between the ages of 2 and 5 were sampled and problemed about their child's television watching habits. Based on these 100 children (between the ages of 2 and 5 years old), the average hours of TV watched weekly was found to be 31 hours with a standard deviation of 9 hours.

a. What is the standard error of the sample mean?
b. Provide the hypotheses the researchers are trying to test, being sure to include a definition of the parameter of interest.
c. Compute the appropriate test statistic value (include its symbol)
d. Interpret the value of the test statistic as a distance in terms of standard errors
e. If the null hypothesis is true, what is the distribution of the test statistic? Be complete
f. What is the corresponding p-value for conducting this test? You may use the table or the pval() script with R to create a picture of and find the p-value and upload it for your work
g. What would your decision be in this case using a 5% significance level?
h. Provide a written conclusion in the context of this study of young children watching television
i. The analyst working on this study remembers that the probability of concluding children do watch more television today when in fact they really do watch more television is an important quantity to consider. What is the statistical name for this quantity?