Find the critical values: a. determine the critical value /2 that corresponds to a level of confidence of 87%. (2 pts). b. find the critical t-value /2 that corresponds to 92% confidence and n = 15. (2 pts). c. determine the critical value for a left-tailed test of a population mean at the α = 0.025 level of significance based on a sample size of n = 18. (2 pts) d. find the critical value for a two-tailed test of a population proportion with α = 0.08. (2 pts)

a) and

b) and

c)

d) and

Step-by-step explanation:

Part a

On this case the confidence is 87% or 0.87 so the significance level is and . 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:

or 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 and

Part b

On this case the confidence is 92% or 0.92 so the significance level is and . 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:

We need values b,c on the t distribution with 14 degrees of freddom such that:

or 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 and

Part c

The significance level is 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:

We need a value c on the t distribution with 17 degrees of freddom such that:

, 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

Part d

The significance level is and . 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:

or 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 and

7

step-by-step explanation:

because they could drop even lower..