Respuesta :
Answer:
a) [tex]z_{\alpha/2}=-1.51[/tex] and [tex]z_{\alpha/2}=1.51[/tex]
b) [tex]t_{\alpha/2}=-1.89[/tex] and [tex]t_{\alpha/2}=1.89[/tex]
c) [tex]t_{\alpha/2}=-2.11[/tex]
d) [tex]z_{\alpha/2}=-1.75[/tex] and [tex]z_{\alpha/2}=1.75[/tex]
Step-by-step explanation:
Part a
On this case the confidence is 87% or 0.87 so the significance level is [tex]\alpha=1-0.87=0.13[/tex] and [tex]\alpha/2 =0.065[/tex]. On this case we can assume that is a bilateral test or a confidence interval so we will have two critical values.
We need values a,b on the normal standard distribution such that:
[tex]P(Z<a)=0.065[/tex] or [tex]P(Z>b)=0.065[/tex] and in order to find it we can use the following code in excel:
"NORM.INV(0.065,0,1)" or "NORM.INV(1-0.065,0,1)", and we see that the critical values [tex]z_{\alpha/2}=-1.51[/tex] and [tex]z_{\alpha/2}=1.51[/tex]
Part b
On this case the confidence is 92% or 0.92 so the significance level is [tex]\alpha=1-0.92=0.08[/tex] and [tex]\alpha/2 =0.04[/tex]. On this case we can assume that is a bilateral test or a confidence interval so we will have two critical values.
First we need to calculate the degrees of freedom given by:
[tex]df=n-1=15-1=14[/tex]
We need values b,c on the t distribution with 14 degrees of freddom such that:
[tex]P(t_{(14)}<b)=0.04[/tex] or [tex]P(t_{(14)}>c)=0.04[/tex] and in order to find it we can use the following code in excel:
"T.INV(0.04,14)" or "T.INV(1-0.04,14)", and we see that the critical values [tex]t_{\alpha/2}=-1.89[/tex] and [tex]t_{\alpha/2}=1.89[/tex]
Part c
The significance level is [tex]\alpha=0.025[/tex] and is a left tailed test. On this case we know that is a left tailed test so then we have just one critical value.
First we need to calculate the degrees of freedom given by:
[tex]df=n-1=18-1=17[/tex]
We need a value c on the t distribution with 17 degrees of freddom such that:
[tex]P(t_{(17)}<c)=0.025[/tex], and in order to find it we can use the following code in excel:
"T.INV(0.025,17)", and we see that the critical values [tex]t_{\alpha/2}=-2.11[/tex]
Part d
The significance level is [tex]\alpha=0.08[/tex] and [tex]\alpha/2 =0.04[/tex]. On this case we know that w ehave a two tailed proportion test, so we will have two critical values.
We need values a,b on the normal standard distribution such that:
[tex]P(Z<a)=0.04[/tex] or [tex]P(Z>b)=0.04[/tex] and in order to find it we can use the following code in excel:
"NORM.INV(0.04,0,1)" or "NORM.INV(1-0.04,0,1)", and we see that the critical values [tex]z_{\alpha/2}=-1.75[/tex] and [tex]z_{\alpha/2}=1.75[/tex]
