Question

To begin answering our original 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 0.01 significance level.

Recall 13 of 40 children in the low income group drew the nickel too large, and 7 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:μL≠μHH1:μL≠μH
• H1:μL<μHH1:μL<μH
• H1:μL>μHH1:μL>μH
• H1:pL<pHH1:pL<pH
• H1:pL>pHH1:pL>pH
• H1:pL≠pHH1:pL≠pH

b) The test statistic value is:   

c) Using the P-value method, the P-value is:

Answer 1

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Answer:

The null and alternative hypothesis is

Given,

p1 = x1/n1

= 13/40

= 0.325

p2 = x2/n2

= 7/35

= 0.2

p = (x1+x2)/(n1+n2)

= (13 + 7)/(40 + 35)

= 0.2666

test statistic = (p1 - p2)/sqrt(p(1-p)*(1/n1 + 1/n2)

substitute values

= (0.325 - 0.2)/sqrt(0.266(1-0.266)*(1/40 + 1/35))

= 1.22

Corresponding P value = 0.1110 [since from z table]

= 0.1110 > 0.01

So we fail to reject Ho.