Question

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​?

Answer 1

Answer:

a) Two tailed test

Null hypothesis:$p=0.217$  

Alternative hypothesis:$p \neq 0.217$  

b) $p_v =2*P(Z>2.17)=0.03$  

c) If we compare the p value obtained and the significance level given $\alpha=0.01$ we have $p_v>\alpha$ 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

$\hat p$ estimated proportion of interest

$p_o$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

$p_v$ 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:$p=0.217$  

Alternative hypothesis:$p \neq 0.217$  

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

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)  

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

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 $\alpha=0.05$. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

$p_v =2*P(Z>2.17)=0.03$  

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 $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

We Fail to reject the null hypothesis H0