Answer to Question #175370 in Statistics and Probability for Adrian Nebreja TOSOC

Question

Question 8

Researchers investigating characteristics of gifted children

collected data from schools in a large city on a random sample of

thirty-six children who were identified as gifted children soon after

they reached the age of four. The following histogram shows the

distribution of the ages (in months) at which these children first

counted to 10 successfully. Also provided are some sample statistics.

Suppose

you read online that children first count to 10 successfully when they

are 32 months old, on average. You perform a hypothesis test evaluating

whether the average age at which gifted children first count to 10 is

different than the general average of 32 months. What is the p-value of

the hypothesis test? Choose the closest answer.

Answer 1

$N=36$

$\overline{x}=30.69$

$\sigma=4.31$

$H_0$ : The mean age is 32 months to count to 10; $\mu=32$

$H_a$ : The mean age is less than 32 months to count to 10; $\mu<32$

Test Statistic:

$z=\frac{\overline{x}-\mu}{\sigma/\sqrt{N}}=\frac{30.69-32}{4.31/\sqrt{36}}=-1.82$

p-value:

$p=P(z<-1.82)=0.034$