# Hypothesis Testing Question: 1 Sided

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.

• you use the z-test because the s.d. is known
– AmR
Jul 7 '18 at 18:33
• How do you know that it's known?
– Hx3
Jul 8 '18 at 0:16
• I get confused when to use the z and t test
– Hx3
Jul 8 '18 at 0:17
• well you use z when the s.d. is known and t when it's unknown. It will be stated
– AmR
Jul 8 '18 at 0:19
• Okay, thanks! @AmR
– Hx3
Jul 8 '18 at 0:24

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.

• How does a random sample of 30 students infer that the students in her class have above average IQs? I know its only academic but to me it's not a very well thought out question. Jul 7 '18 at 18:58
• Yeah i really didn't like the way it was worded.
– AmR
Jul 7 '18 at 19:40
• I up voted your answer for the math procedure and for the fact that you steered clear of making a summary conclusion. Jul 7 '18 at 19:58
• My teacher uses this example for all the classes she teaches
– Hx3
Jul 8 '18 at 0:15
• My older brother had her 4 years ago and he remembers having that question
– Hx3
Jul 8 '18 at 0:20

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.