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Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate:_________.
(a) find the critical value t Subscript alpha divided by 2 tα/2​, ​
(b) find the critical value z Subscript alpha divided by 2 zα/2​, or​
(c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn​ girls: n equals = 236​, x overbar x equals = 30.3 ​hg, s equals = 7.2 hg. The confidence level is 95​%.
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A. t Subscript alpha divided by 2 tα/2 equals = nothing ​(Round to two decimal places as​ needed.)
B. z Subscript alpha divided by 2 zα/2 equals = nothing ​(Round to two decimal places as​ needed.)
C. Neither the normal distribution nor the t distribution applies.

Respuesta :

Answer:

B. z Subscript alpha divided by 2 zα/2 = 1.96.

Step-by-step explanation:

We are given that we want to construct a confidence interval. For this, the summary statistics for randomly selected weights of newborn​ girls:

n = 236​, [tex]\bar x[/tex] = 30.3 ​hg, s = 7.2 hg. The confidence level is 95​%.

As we can clearly see here that the population standard deviation is unknown and the sample size is also very large.

It has been stated that when the population standard deviation is unknown, we should use t-distribution but since the sample size is very large so we can use z distribution also as it is stated that at very large samples; the t-distribution corresponds to the z-distribution.

Here, [tex]\alpha[/tex] = level of significance = 1 - 0.95 = 0.05 or 5%

         [tex]\frac{\alpha}{2}=\frac{0.05}{2}[/tex] = 0.025 or 2.5%

So, the value of [tex]Z_(_\frac{\alpha}{2} _)[/tex] in the z table is given as 1.96 with a 2.5% level of significance.