Question

Boys of a certain age in the nation have an average weight of 86 with a standard deviation of 9.6 lb. A complaint is made that boys are overfed in a municipal children's home. As evidence, a sample of 29 boys of the given age is taken from the children's home with an average weight of 85.14 lb. What can be concluded with α = 0.01?

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test
Population:
---Select--- children's home boys from the home feeding method boys in the nation weight
Sample:
---Select--- children's home boys from the home feeding method boys in the nation weight

b) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

c) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]
Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

The average weight of boys in the municipal children's home was significantly higher than the average weight of boys in the nation.The average weight of boys in the municipal children's home was significantly lower than the average weight of boys in the nation.    The average weight of boys in the municipal children's home was not significantly different than the average weight of boys in the nation.

Answer 1

Given the sample size and sample mean , population standard deviation .

Since the population standard deviation is known, we cam use z-distribution.

a) The test to be used is : One-Sample z-test

b)The hypotheses are

The claim is the null hypothesis.

The appropriate test statistic is

The critical value is .

Since the critical value is less than the test statistic, we Fail to reject H0.

c) There is no need of computing the CI since this is a one-tailed test, and we have calculated the test statistic.

NA.

NA

d) The correct choice is

The average weight of boys in the municipal children's home was significantly higher than the average weight of boys in the nation.