Answer:
The critical z value used to test a null hypothesis is ±1.75.
Step-by-step explanation:
We are given that the data has a normal distribution and the number of observations is greater than fifty.
Also, the hypothesis given to us is;
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 3.24
Alternate Hypothesis, [tex]H_1[/tex] : [tex]\mu\neq[/tex] 3.24
This means that our test is two-tailed because in the alternate hypothesis we are concerned with mean value is less than or greater than 3.24.
Also, level of significance (α) = 0.08
Now, for two-tailed test level of significance becomes = [tex]\frac{\alpha}{2} =\frac{0.08}{2}[/tex] = 0.04
So, in the z-table the critical value of x at 4% significance level is given as 1.75.
Since, this is two-tailed test so the critical z value used to test a null hypothesis would be ±1.75.
At the 4% significance level, the z-value is 1.75. Therefore, for the two tailed test the z value becomes [tex]\pm[/tex] 1.75. and this can be determined by using the given data.
Given :
According to the hypothesis test:
Null Hypothesis -- [tex]\rm H_0:\mu=3.24[/tex]
Alternate Hypothesis -- [tex]\rm H_1 : \mu\neq 3.24[/tex]
According to the given data, the significance level is given by α = 0.08. So, the significance level for the two tailed test is given by:
[tex]\rm \dfrac{\alpha }{2}=\dfrac{0.08}{2}=0.04[/tex]
So, for the 4% significance level, the z-value is 1.75. Therefore, for the two tailed test the z value becomes [tex]\pm[/tex] 1.75.
So, the correct option is a).
For more information, refer to the link given below:
https://brainly.com/question/2253924
