Question

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​?

Answer 1

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<-2.326`

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.

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{(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<-2.326`

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.