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

a) Two tailed test

Null hypothesis:
`p=0.217`

Alternative hypothesis:
`p \\eq 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

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 \\eq 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{(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