A reseacher conducted a study to explore whether perception of money by preschoo

Question

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:L>HH1:L>H

H1:pL>pHH1:pL>pH

H1:L<HH1:L<H

H1:pLpHH1:pLpH

H1:LHH1:LH

H1:pL<pHH1:pL<pH

The researcher had preschool children from low and high income groups draw nickels. It was found that 22 of 40 children in the low income group drew the nickel too large, while 12 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

The sample data supports the claim

There is not sufficient evidence to support the claim

There is not sufficient evidence to warrant rejection of the claim

There is sufficient evidence to warrant rejection of the claim

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 > 0

Hypothesis test results:

Hence,

a) Correct alternative hpothesis:

H1: pL > pH

b) Test statistic = 1.798

c) P - value = 0.0361

d) Fail to reject Ho

e) There is not sufficient evidence to support the claim. Option B is correct.

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