Question

A researcher knows that the weights of 6 year olds are normally distributed with μ = 20 kg and

σ = 5.0. She suspects that children in poverty-stricken regions differ from the population. With a sample of n = 25 children, the researcher obtains a mean of 17 kg.  

a. State the null hypothesis.

b. Identify the appropriate statistical test

c. Calculate the appropriate test statistic. Make sure to report the degrees of freedom for the statistical test (if appropriate). You must show your work to receive full credit.

d. State your conclusions (use a two-tailed test with  = .05 for all tests).

e. Compute an effect size

Answer 1

a. The null and alternative hypothesis is ,

b) Since , the population standard deviation is known.

Therefore , use normal distribution.

Therefore , use two-tailed Z-test.

c) The test statistic is ,

d) The critical values are ,

; From Z-table

Decision : Here , the value of the test statistic lies in the rejection region.

Therefore , reject the null hypothesis.

Conclusion : Hence , she suspects that children in poverty-stricken regions differes from the population.

e) Effect size=