A teacher at a school claims that the students in her class are above average intelligence. A random sample of 30 students IQ scores have a mean score of 112. Is there sufficient evidence to support the teacher's claim? The mean population IQ is 100 with a standard deviation of 15.
The alpha level = 0.05
The critical value = 1.645
I don't know what formula to use to find the test statistics.
On
Since the standard deviation of 15 is known, you would use the formula: $Z=\frac{\bar{x}-μ}{σ/\sqrt{n}}$. Where $\bar{x}$ = 112, $μ = 100$, $σ = 15$, and $n = 30$.
If the test statistic is less than the critical value, you fail to reject the null. If test statistic is greater than the critical value, you reject the null.
1) State the null and alternate hypothesis:
$H_0:μ = 100$
$H_1:μ > 100$
2) Find the alpha level. There was no alpha level given so by default we use $0.05$.
3) Find the reject region (critical value). By using the z-table, the area of $0.05$ is equal to the z-score of $1.645$.
4) Find the test statistic.
$Z=\frac{\bar{x}-μ}{σ/\sqrt{n}}$
= $\frac{112.5-100}{15/\sqrt{30}}$
= 4.56
5) Since the test statistics of 4.56 is greater than the critical value of 1.645, we reject the null hypothesis.