Mathematics, 03.12.2019 04:31 chloe081

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)

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Answer from: firefightergros3547

a) $z_{\alpha/2}=-1.51$ and $z_{\alpha/2}=1.51$

b) $t_{\alpha/2}=-1.89$ and $t_{\alpha/2}=1.89$

c) $t_{\alpha/2}=-2.11$

d) $z_{\alpha/2}=-1.75$ and $z_{\alpha/2}=1.75$

Step-by-step explanation:

Part a

On this case the confidence is 87% or 0.87 so the significance level is $\alpha=1-0.87=0.13$ and $\alpha/2 =0.065$ . 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:

P(Z or P(Zb)=0.065 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 $z_{\alpha/2}=-1.51$ and $z_{\alpha/2}=1.51$

Part b

On this case the confidence is 92% or 0.92 so the significance level is $\alpha=1-0.92=0.08$ and $\alpha/2 =0.04$ . 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:

df=n-1=15-1=14

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

$P(t_{(14)}$ or $P(t_{(14)}c)=0.04$ 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 $t_{\alpha/2}=-1.89$ and $t_{\alpha/2}=1.89$

Part c

The significance level is $\alpha=0.025$ 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:

df=n-1=18-1=17

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

$P(t_{(17)}$ , 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 $t_{\alpha/2}=-2.11$

Part d

The significance level is $\alpha=0.08$ and $\alpha/2 =0.04$ . 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:

P(Z or P(Zb)=0.04 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 $z_{\alpha/2}=-1.75$ and $z_{\alpha/2}=1.75$

Answer from: Quest

i will take them

step-by-step explanation:

Answer from: Quest

Ithink you're supposed to multiply 12.50 which is how much he makes per hour and then multiply it by each number then add whats left togrther and there's your answer

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