A reseacher conducted a study to explore whether perception of money by preschool aged children is influenced by their family's income status. The study tested the claim that the proportion of children from a low income group that drew the nickel too large, is greater than the proportion of the high income group that drew the nickel too large. You are asked to conduct the analysis and test the claim at the 0.01 significance level.
a) If we use LL to denote the low income group and HH to denote the high income group, identify the correct alternative hypothesis.
- H1:μL>μHH1:μL>μH
- H1:pL
- H1:pL≠pHH1:pL≠pH
- H1:pL>pHH1:pL>pH
- H1:μL<μHH1:μL<μH
- H1:μL≠μHH1:μL≠μH
The researcher had preschool children from low and high income groups draw nickels. It was found that 27 of 40 children in the low income group drew the nickel too large, while 8 of 35 in the high income group drew the nickel too large.
b) The test statistic value is:
c) Using the P-value method, the P-value is:
d) Based on this, we
- Reject H0H0
- Fail to reject H0H0
e) Which means
- There is sufficient evidence to warrant rejection of the claim
- There is not sufficient evidence to warrant rejection of the claim
- There is not sufficient evidence to support the claim
- The sample data supports the claim