The u. s. bureau of labor statistics reports that 11.3% of u. s. workers belong to unions. suppose a sample of 400 u. s. workers is collected in 2014 to determine whether union efforts to organize have increased union membership at 0.025 level of significance. the sample results in a test statistic (z) of 2.2.

we conclude that union membership increased in 2014. (enter 1 if the conclusion is correct. enter 0 otherwise.)

1. The conclusion is statistically correct at the significance level given.

Step-by-step explanation:

1) Data given and notation n  

n=400 represent the random sample taken  

X represent the people with union membership in the sample

estimated proportion of people with union membership in the sample

is the value that we want to test  

represent the significance level (no given)  

z would represent the statistic (variable of interest)  

represent the p value (variable of interest)  

p= population proportion of people with union membership

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion of people with union membership exceeds 11.3%. :  

Null Hypothesis:

Alternative Hypothesis:

We assume that the proportion follows a normal distribution.  

This is a one tail upper test for the proportion of  union membership.

The One-Sample Proportion Test is "used to assess whether a population proportion is significantly (different,higher or less) from a hypothesized value ".

Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

3) Calculate the statistic  

The statistic is calculated with the following formula:

On this case the value of is the value that we are testing and n = 400.

Since we have already the statistic calculated z=2.2, we just need to calculate the p value in order to check if we can reject or not the null hypothesis.

4) 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.  

Based on the alternative hypothesis the p value would be given by:

Using the significance level given we see that so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the union membership increased in 2014.

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step-by-step explanation: