# 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. which of the following are appropriate hypotheses for the researcher?

**Question: 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. which of the following are appropriate hypotheses for the researcher?**

In this blog post, I will discuss a research question that I am interested in: How prevalent is charitable giving in a certain city? To answer this question, I have collected data from a simple random sample of households in the city and asked them whether they gave a charitable donation in the past year. My goal is to test whether the proportion of households that gave a donation is higher than 50 percent, which is the expected value under the assumption of no difference.

To perform this test, I need to set up two hypotheses: the null hypothesis and the alternative hypothesis. The null hypothesis is the statement that there is no difference between the observed proportion and the expected proportion, or in other words, that the proportion of households that gave a donation is equal to 50 percent. The alternative hypothesis is the statement that there is a difference, or in this case, that the proportion of households that gave a donation is greater than 50 percent.

Using mathematical notation, I can write these hypotheses as follows:

H0: p = 0.5

Ha: p > 0.5

where p represents the proportion of all households in the city that gave a charitable donation in the past year.

These hypotheses are appropriate for my research question because they allow me to test whether there is convincing statistical evidence that more than half of the households in the city are charitable donors. If I reject the null hypothesis, I can conclude that there is a significant difference between the observed proportion and the expected proportion, and that the observed proportion is higher than 50 percent. If I fail to reject the null hypothesis, I cannot conclude anything about the difference, and I have to accept that the observed proportion could be equal to or lower than 50 percent.

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