Respuesta :
Answer:
a) Since we are conducting a left tailed test and the significance level is [tex]\alpha=0.01[/tex] we need to find a critical value on the left tail that accumulate 0.01 of the area on the left and we got [tex] z_{cric}= -2.326[/tex]
And the rejection zone of the null hypothesis would be [tex] z<-2.326[/tex]
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:[tex]p\geq 0.33[/tex]
Alternative hypothesis:[tex]p < 0.33[/tex]
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
For this case the statistic calculated is [tex]z_{calc}= -3.33[/tex]
Part a
Since we are conducting a left tailed test and the significance level is [tex]\alpha=0.01[/tex] we need to find a critical value on the left tail that accumulate 0.01 of the area on the left and we got [tex] z_{cric}= -2.326[/tex]
And the rejection zone of the null hypothesis would be [tex] z<-2.326[/tex]
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.
