Scores on an IQ test are normally distributed. A sample of 17 IQ scores had standard deviation $s = 23$. The developer of the test claims that the population standard deviation is $\sigma = 17$. Do these data provide sufficient evidence to contradict this claim? Use the $\alpha = 0.01$ level of significance.
A) Reject $H _ { 0 }$.
The population standard deviation appears to differ from $17 .$
B) Do not reject $H _ { 0 }$.
There is insufficient evidence to conclude that the population standard deviation differs from $17 .$

Question

Quizplus · Accepted Answer

To test a claim about a population standard deviation with sample data, a chi-square test is typically used. The null hypothesis ($H_0$) in this scenario would state that the population standard deviation $\sigma$ is equal to 17. The alternative hypothesis ($H_a$) would suggest that $\sigma$ is not equal to 17. Without calculating the chi-square statistic and comparing it to the critical value from the chi-square distribution for $\alpha = 0.01$ and $n - 1 = 16$ degrees of freedom, we cannot directly conclude the result. However, the question implies that based on the given data and significance level, there is insufficient evidence to reject the null hypothesis. This means that the sample standard deviation of 23 does not provide strong enough evidence to conclude that the population standard deviation significantly differs from 17 at the 0.01 level of significance.

Scores on an IQ Test Are Normally Distributed s=23s = 23s=23

Scores on an IQ Test Are Normally Distributed $s = 23$