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14 August, 05:48

A researcher is conducting a study of charitable donations by surveying a simple random sample of households in a certain city. The researcher wants to determine whether there is convincing statistical evidence that more than 50 percent of households in the city gave a charitable donation in the past year. Let p represent the proportion of all households in the city that gave a charitable donation in the past year.

Determine the appropriate hypotheses for the researcher.

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  1. 14 August, 06:11
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    H0: p ≤ 0.50

    Ha: p > 0.50

    Step-by-step explanation:

    The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

    For the case above;

    Let p represent the proportion of households in the city that gave a charitable donation in the past year

    The null hypothesis is that the proportion of households in the city that gave a charitable donation in the past year is not more that 0.50

    H0: p ≤ 0.50

    The alternative hypothesis is that the proportion of households in the city that gave a charitable donation in the past year is more that 0.50

    Ha: p > 0.50
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