In 1996 31 of elementary students reported that their mother

In 1996, 31% of elementary students reported that their mothers had graduated from college. In 2000, responses from 8368 found that this figure grown to 32%. Is this evidence of a change in education level among mothers?

a. Define the population proportion of interest.

b. State hypothesis

c. check conditions

d. Find the test statistics

e. Find the P-value

f. Do you reject or fil to reject Ho at the .05 significance level?

g. Make a condition in the context of the original problem.

h. What type of error could you have made?

i. Is this change significant practically?

Solution

a. Define the population proportion of interest.

All elementary students reported that their mothers had graduated from college

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b. State hypothesis

Ho: p=0.31 (i.e. null hypothesis)

Ha: p not equal to 0.31 (i.e. alternative hypothesis)

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c. check conditions

We need to assume that the population follows Normal distribution

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d. Find the test statistics

Z=(phat-p)/sqrt(p*(1-p)/n)

=(0.32-0.31)/sqrt(0.31*(1-0.31)/8368)

=1.98

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e. Find the P-value

It is a two-tailed test.

So the p-value= 2*P(Z>1.98) = 0.0477 (from standard normal table)

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f. Do you reject or fil to reject Ho at the .05 significance level?

Since the p-value is less than 0.05, we reject Ho.

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g. Make a condition in the context of the original problem.

So we can conclude that this is evidence of a change in education level among mothers

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h. What type of error could you have made?

Type I error.

We reject Ho when it is true.

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i. Is this change significant practically?

Yes.