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The number of people who were given a $1 bill/4 quarters and who spent the money is tabulated along with the individual sample sizes.

It is claimed that money in a large denomination is less likely to be spent relative to the same amount of money in smaller denominations.

Since the given claim does not have an equality sign, the following hypotheses are set up:

Null Hypothesis: The proportion of people who spend the money is equal and does not depend on its denomination.

\({H_0}:{p_1} = {p_2}\)

Alternative Hypothesis: The proportion of people who spend the money when they receive a large denomination ($1 bill) is less than the proportion of people who spend the money when they receive smaller denominations (4 quarters).

\({H_1}:{p_1} < {p_2}\)

The test is left-tailed.

If the absolute value of the test statistic is greater than the critical value, the null hypothesis is rejected.

Let\({\hat p_1}\)denote the sampleproportion of people who received a $1 bill and spent it.

\(\begin{aligned}{c}{{\hat p}_1} &= \frac{{{\rm{Number}}\;{\rm{of}}\;{\rm{people}}}}{{{\rm{Sample}}\;{\rm{size}}}}\\ &= \frac{{{x_1}}}{{{n_1}}}\\ &= \frac{{12}}{{46}}\\ &= 0.261\end{aligned}\)

Let\({\hat p_2}\)denote the sampleproportion of people who received 4 quarters and spent the money.

\(\begin{aligned}{c}{{\hat p}_2} &= \frac{{{\rm{Number}}\;{\rm{of}}\;{\rm{people}}}}{{{\rm{Sample}}\;{\rm{size}}}}\\ &= \frac{{{x_2}}}{{{n_2}}}\\ &= \frac{{27}}{{43}}\\ &= 0.628\end{aligned}\)

\({n_1}\)is equal to 46 and\({n_2}\)is equal to 43.

The value of the pooled sample proportion is computed as follows:

\(\begin{aligned}{c}\bar p &= \frac{{{x_1} + {x_2}}}{{{n_1} + {n_2}}}\\ &= \frac{{12 + 27}}{{46 + 43}}\\ &= 0.438\end{aligned}\)

\(\begin{aligned}{c}\bar q &= 1 - \bar p\\ &= 1 - 0.438\\ &= 0.562\end{aligned}\)

The value of the test statistic is computed below:

\(\begin{aligned} z &= \frac{{\left( {{{\hat p}_1} - {{\hat p}_2}} \right) - \left( {{p_1} - {p_2}} \right)}}{{\sqrt {\frac{{\bar p\bar q}}{{{n_1}}} + \frac{{\bar p\bar q}}{{{n_2}}}} }}\;\;\;\;{\rm{where}}\left( {{p_1} - {p_2}} \right) &= 0\\ &= \frac{{\left( {0.261 - 0.628} \right) - 0}}{{\sqrt {\frac{{\left( {0.438} \right)\left( {0.562} \right)}}{{46}} + \frac{{\left( {0.438} \right)\left( {0.562} \right)}}{{43}}} }}\\ &= - 3.49\end{aligned}\)

Thus, z= 鈥�3.49.

Using the standard normal table, the critical value of z corresponding to\(\alpha = 0.05\)for a left-tailed test is equal to 鈥�1.645.

The corresponding p-value is equal to 0.0002 which is obtained from the standard normal table using the test statistic (鈥�3.49).

Since the absolute z-score value is greater than the critical value and the p-value is less than 0.05, the null hypothesis is rejected.

There is enough evidence to support the claim thatmoney in a large denomination is less likely to be spent relative to the same amount of money in smaller denominations.