Question

State the null and alternative hypotheses for the statistical test described below. Your answer should be an expression composed of symbols: Testing to see if there is evidence that a proportion is greater than 0.3.
H0: ____ vs Ha: ______

Answer 1

Answer:

Null hypothesis: $p \leq 0.3$

Alternative hypothesis: $p>0.3$

Step-by-step explanation:

For this question we need to take in count that the the claim that they want to test is "if the proportion is greater than 0.3". Our parameter of interest for this case is $p$ and the estimator for this parameter is given by this statistic $\hat p$ obtained from the info of sa sample obtained.

The sample proportion would be given by:

$\hat p = \frac{X}{n}$

Where X represent the success and n the sample size selected

The alternative hypothesis on this case would be specified by the claim and the complement would be the null hypothesis. Based on this the system of hypothesis for this case are:

Null hypothesis: $p \leq 0.3$

Alternative hypothesis: $p>0.3$

And in order to check the hypothesis we can use the one sample z test for a proportion with the following statistic:

$z = \frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}$