Answer :
To determine the z values for a two-tailed test at a 0.0910 level of significance, we need to understand how the significance level affects the critical z values in a standard normal distribution.
Understanding the Level of Significance:
The level of significance, often denoted by [tex]\alpha[/tex], is the probability of rejecting the null hypothesis when it is actually true. In a two-tailed test, this significance level is split equally between the two tails of the normal distribution.Splitting the Significance Level:
Given [tex]\alpha = 0.0910[/tex], we split this into two tails, meaning each tail has an area of [tex]\frac{0.0910}{2} = 0.0455[/tex].Finding the Critical Z Values:
We need to find the z values that correspond to the cumulative area of [tex]0.0455[/tex] in the lower tail and [tex]1 - 0.0455 = 0.9545[/tex] in the upper tail of the standard normal distribution.The z value for a left tail of [tex]0.0455[/tex] is approximately [tex]-1.69[/tex], and for a right tail of [tex]0.9545[/tex], it is approximately [tex]1.69[/tex].
Thus, the correct z values for the two-tailed test at a 0.0910 level of significance are approximately [tex]-1.69[/tex] and [tex]1.69[/tex]. Therefore, the correct option is: (b) –1.69 and 1.69.
