Answer:
1) The correct z* to to construct a 92% confidence interval is 1.75
2) these results are not good evidence that the new curriculum has improved Math SAT scores.
3) the results are not statistically significant at level α = 0.05, but they are practically significant.
Step-by-step explanation:
1) z-score for 92% confidence level is ≈ 1.75
2) P-value for testing whether the mean score in senator's state is more than the national average of 480 is less than 0.0001 means that
the probability that the sample is drawn from the population where senator's state is more than the national average of 480 is <0.0001.
Thus we have to reject this hypothesis since the probability is too small.
3) if we calculate the statistic of the sample we get (560-480)/100=0.8 where
- 560 is the mean score of trained 4 students
- 480 is the mean math sat score of this year
- 100 is the standard deviation of the test.
Since t-critical at 0.05 significance for 3 degrees of freedom ≈ 2.35 is bigger than 0.8, the result is not significant statistically.
But 80 points higher than the national average is a practically significant result since its <em>effect size</em> is large.
