The weight (in pounds) for a population of school-aged children is normally dist

Question

The weight (in pounds) for a population of school-aged children is normally distributed with a mean equal to 135 pound and standard deviation of 20. We select a sample of 100 children with a mean of 140 pounds to test whether children in this population are gaining weight at a .05 level of significance.

Answer each of the following questions:

What is the null hypothesis?

What is/are the critical values?

What is the standard error?

What is the test statistic?

Explain why you would retain or reject the null hypothesis? Provide the probability.

Would you calculate Cohen’s d? Why or why not?

Compute the value and the effect size of Cohen’s d.

Explanation / Answer

What is the null hypothesis?

H0: µ 135

What is the critical value?

Here it is one-tailed z-test. The level of significance is .05. From normal table we get the critical value as 1.645.

Critical value = 1.645

What is the standard error:

SE = s / sqrt (n) = 20 / sqrt (100) = 20 / 10 = 2

Standard error = 2

What is the test Statistics?

Z = ( x bar – Mew )/(sigma / sqrt(n))

   = (140 – 135)/2

   = 2.5

The value of test statistics is 2.5

Explain why you would retain or reject the null hypothesis?

Here we reject the null hypothesis as the test statistics value is greater than the critical value (2.50>1.645).

Would you calculate Cohen’s d?

Yes, we can find it as it gives an effect size used to indicate the standardised difference between two means.

Compute the value and the effect size of Cohen’s D.

Cohen’s D = (140-135)/20

                 = 0.25

Cohen’s D = 0.25

Here the effect size is a small effect size.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.