Question

The test statistic of zequalsnegative 3.33 is obtained when testing the claim that less than 0.33.

Answer 1

Answer:

a) Since we are conducting a left tailed test and the significance level is $\alpha=0.01$ we need to find a critical value on the left tail that accumulate 0.01 of the area on the left and we got $z_{cric}= -2.326$

And the rejection zone of the null hypothesis would be $z$

b) For this case since the statistic calculated is -3.33 <--2.326 we have enough evidence to reject the null hypothesis at 1 % of significance for this case.

Step-by-step explanation:

1) Concepts and formulas to use  

We can asume that we need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.33:  

Null hypothesis:$p\geq 0.33$  

Alternative hypothesis:$p < 0.33$  

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 calculated is $z_{calc}= -3.33$

Part a

Since we are conducting a left tailed test and the significance level is $\alpha=0.01$ we need to find a critical value on the left tail that accumulate 0.01 of the area on the left and we got $z_{cric}= -2.326$

And the rejection zone of the null hypothesis would be $z$

Part b

For this case since the statistic calculated is -3.33 <--2.326 we have enough evidence to reject the null hypothesis at 1 % of significance for this case.