Question

The test statistic of zequals2.32 is obtained when testing the claim that pgreater than0.3. a. Identify the hypothesis test as being​ two-tailed, left-tailed, or​ right-tailed. b. Find the​ P-value. c. Using a significance level of alphaequals0.10​, should we reject Upper H 0 or should we fail to reject Upper H 0​?

Answer 1

Answer:

a) We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:  

Null hypothesis:$p \leq 0.3$  

Alternative hypothesis:$p > 0.3$  

Right tailed test

b) $p_v =P(z>2.32)=0.0102$  

c) So the p value obtained was a very low value and using the significance level given $\alpha=0.1$ we have $p_v<\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3

Step-by-step explanation:

Part a: Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:  

Null hypothesis:$p \leq 0.3$  

Alternative hypothesis:$p > 0.3$  

Right tailed test

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

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

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$.

Calculate the statistic  

For this case the statistic is given by $z_{calc}= 2.32$

Part b: Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

$p_v =P(z>2.32)=0.0102$  

Part c

So the p value obtained was a very low value and using the significance level given $\alpha=0.1$ we have $p_v<\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3