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

The estimated standard error (SM) for the sample of 27 girls is 1.1547 years, and the t statistic calculated to test if there is a difference in the age at which developmentally delayed girls reach their adult height is approximately 0.95.

Step-by-step explanation:

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 girls. The average age at which adolescent girls reach their adult height is generally 16 years. For the sample of 27 girls with developmental delays, they have reached their adult height at an average age of 17.1 years with a sample variance of 36.0 years.

To calculate the t statistic, we first need to calculate the estimated standard error. The estimated standard error (SM) is calculated using the formula SM = s / √n, where s is the sample standard deviation and n is the sample size. Since the sample variance is 36.0, the standard deviation (s) is the square root of the variance, which is 6.0 years.

So, SM = 6.0 / √27, which results in an estimated standard error of 1.1547 years.

Next, to calculate the t statistic, we use the formula: t = (M - μ) / SM, where M is the sample mean, μ is the population mean (assumed to be 16 years for this hypothesis test), and SM is the estimated standard error the we just calculated.

Using the given values, t = (17.1 - 16) / 1.1547, which gives us a t statistic of approximately 0.95.

Answer 2

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=(s)/(√(n))=(6)/(√(27))=1.1547`

Then, we can calculate the t-statistic as:

`t=(M-\mu)/(s/√(n))=(17.7-16)/(1.1547)=(1.7)/(1.1547)=1.4722`