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.

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