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

a. Using a significance level of alpha=0.01, find the critical value(s).
b. Should we reject H0 or should we fail to reject H0?

a) Since we are conducting a left tailed test and the significance level is we need to find a critical value on the left tail that accumulate 0.01 of the area on the left and we got

And the rejection zone of the null hypothesis would be

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:  

Alternative hypothesis:  

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

(1)  

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

Calculate the statistic  

For this case the statistic calculated is

Part a

Since we are conducting a left tailed test and the significance level is we need to find a critical value on the left tail that accumulate 0.01 of the area on the left and we got

And the rejection zone of the null hypothesis would be

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.

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Step-by-step explanation: