Question

The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 27 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.1 years and a sample variance of 36.0 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girlCalculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is SM______ . The t statistic is_________

Answer 1

Answer:

The estimated standard error is SM=1.1547 . The t statistic is 1.4722.

Step-by-step explanation:

We have to esimate the standard error and test statistic for a sample.

The sample has a size n=27.

The sample mean is M=17.7.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√36=6.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6}{\sqrt{27}}=1.1547$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{17.7-16}{1.1547}=\dfrac{1.7}{1.1547}=1.4722$