Question

Test the claim that the proportion of children from the 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. Test at the 0.05 significance level.

18 of 40 children in the low income group drew the nickel too large, and 13 of 35 did in the high income group.

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:pL<pHH1:pL<pH
• H1:pL>pHH1:pL>pH
• H1:pL≠pHH1:pL≠pH
• H1:μL<μHH1:μL<μH
• H1:μL≠μHH1:μL≠μH
• H1:μL>μHH1:μL>μH

b) The test statistic value is (two decimal places):

c) Using the P-value method, the P-value is (4 decimal places):

d) Based on this, we

• Reject H0H0
• Fail to reject H0H0

e) Which means

• There is not sufficient evidence from the sample data to warrant rejection of the claim
• The sample data supports the claim
• There is sufficient evidence from the sample data to warrant rejection of the claim
• There is not sufficient evidence from the sample data to support the claim

Answer 1

The statistical software output for this problem is:

Hence,

a) H1: pL>pH

b) Test statistic = 0.69

c) P-value = 0.2453

d) Fail to reject Ho

e) There is not sufficient evidence from the sample data to support the claim. Option D is correct.