In 2017, the average reading score of the fourth graders in the United States was 222 points. In a simple random sample of 16,000 fourth graders taken nationally in 2019, the average reading score is 221 and the SD is 40 points. Is the national average reading score for fourth graders in 2019 different from what it was in 2017? Or is the observed difference just chance variation? Perform a test of hypotheses to answer the question, in the following steps. a) State an appropriate null hypothesis in non-technical terms and also as a set of assumptions about random variables.
b) State an appropriate alternative hypothesis.
c) What test statistic are you going to use? Justify your choice
d) Find an exact or approximate p-value.
e) At the 5% level, what is the conclusion of the test? Why?