The test statistic of z equals=2.17 is obtained when testing the claim that pnot equals≠0.2170.217. a. identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. b. find the p-value. c. using a significance level of alphaαequals=0.010.01, should we reject upper h 0h0 or should we fail to reject upper h 0h0?

a) Two tailed test

Null hypothesis:  

Alternative hypothesis:  

b)  

c) If we compare the p value obtained and the significance level given we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

We Fail to reject the null hypothesis H0

Step-by-step explanation:

Data given and notation

n represent the random sample taken

X represent the outcomes desired in the sample

estimated proportion of interest

is the value that we want to test

represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion is 0.217 or no:  

a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

Two tailed test

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

(1)  

The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .

Calculate the statistic  

For this case the calculated value is given z =2.17  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

b. Find the P-value

The significance level provided . The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

c. Using a significance level of alphaαequals=0.01, should we reject Upper H 0 or should we fail to reject Upper H 0?

If we compare the p value obtained and the significance level given we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

We Fail to reject the null hypothesis H0

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2