In the state of Kentucky, the mean SAT math score is 600 with standard deviation 75....
In the state of Kentucky, the mean SAT math score is 600 with standard deviation 75. A school system in Smithville decides to study if their scores are statistically less than the state. They gather data from 51 students in their district.
| Mean | 536.72549 |
|---|---|
| Std Dev | 33.670805 |
| Std Err Mean | 4.7148558 |
| Upper 95% Mean | 546.19556 |
| Lower 95% Mean | 527.25542 |
| N | 51 |
| Hypothesized Value | 600 |
|---|---|
| Actual Estimate | 536.725 |
| DF | 50 |
| Std Dev | 33.6708 |
| Sigma given | 75 |
| z Test | |
|---|---|
| Test Statistic | -6.0249 |
| Prob > |z| | <.0001* |
| Prob > z | 1.0000 |
| Prob < z | <.0001* |
Question: The state decides to use a lower one-tailed test using α = 0.05. Find the correct critical value and the correct test statistic. (Round your answers to three decimal places.)
critical value =
test statistic =
Homework Answers
Critical value = -1.645
test statistics:
z = (xbar - mu)/(s/sqrt(n))
= ( 536.725 - 600)/(75/sqrt(51))
= -6.025
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