Question

Gun rights vs. gun control: In a December 2014 report, "For the first time in more than two decades of Pew Research Center surveys, there is more support for gun rights than gun control." According to a Pew Research survey, 52% of Americans say that protecting gun rights is more important than controlling gun ownership. Gun control advocates in an urban city believe that the percentage is lower among city residents and conduct a survey. They test the hypotheses H 0: p = 0.52 versus H a: p < 0.52. They calculate a P‐value of 0.078. Using a significance level of 0.05, which of the following is the best explanation for how to use the P‐value to reach a conclusion in this case? Group of answer choices Since the P‐value is greater than the significance level, we reject the null hypothesis. Since the P‐value is greater than the significance level, we fail to reject the null hypothesis. Since the P‐value is greater than the significance level, we accept the null hypothesis.

Answer 1

P-value is greater than alpha, the significance level thus we fail to reject the null hypothesis.

Explanation:

We are given the following information in the question:

`H_0 = 0.52\\H_a < 0.52`

P-Value = 0.078

`Alpha, ~\alpha = 0.05`

We have to reach on a conclusion on the basis of p-value.

P-Value is the probability of finding an observation, basically, it could ne said the probability when the null hypothesis is true.

Alpha is the significance level.

So, if the p-value is greater than the chosen significance level, we fail to reject the null hypothesis and accept it and if the p-value is smaller than the significance level then we reject the null hypothesis and accept the alternate hypothesis.

Since
`P-Value > \alpha`

P-value is greater than alpha, the significance level thus we fail to reject the null hypothesis.