Question

A researcher knows that the body weights of 6-year olds in the state is normally distributed with µ = 20.9 kg and σ = 3.2.  She suspects that children in a certain school district are different.  With a sample of n = 16 children, the researcher obtains a sample mean of M = 22.8.  

1. State the Independent and Dependent Variables
2. State the Null Hypothesis in words and symbols.

b State the alternative Hypothesis in words and symbols.

3. Compute the appropriate statistic.
4. What is the decision (Retain or Reject)
5. State the full conclusion in words

Effect

Direction

Size of Effect

Use a two-tailed test and the .05 of significance to determine if the weights for this sample are significantly higher  than what would be expected for the regular population of 6-year- olds.

Answer 1

Sol:

Depeendent variable: children in a certain school district

Independent variable: body weights of 6-year olds in the state

1. State the Null Hypothesis in words and symbols.

Ho:Mu=20.9

weight of children in a certain school district is same as  body weights of 6-year olds in the state i

b State the alternative Hypothesis in words and symbols.

weight of children in a certain school district is different from body weights of 6-year olds in the state

Ha:mu not =20.9

Compute the appropriate statistic.

z=xbar-mu/sigma/sqrt(n)

=(22.8-20.9)/(3.2/sqrt(16))

z=2.375

What is the decision (Retain or Reject)

critical z for 95% two tail is -1.96,+1.96

test statistic is greater than critical value)

Reject null hypothesis

Decision:

Reject null hypothesis

1. State the full conclusion in words

Effect

effect=sample mean-popualtion mean/sigma

=(22.8-20;9)/3.2

  = 0.59375

Direction:positive

Size of Effect:medium

Conlcusion:

there is suffcient statistical evidence at 5% level of significance to conlcude that

fthe weights for this sample are significantly higher  than what would be expected for the regular population of 6-year- olds.