In a recent year, a poll asked 2362 random adult citizens of a large country how they rated economic conditions. in the poll, 22% rated the economy as excellent/good. a recent media outlet claimed that the percentage of citizens who felt the economy was in excellent/good shape was 24%. does the poll support this claim? a) test the appropriate hypothesis. find a 99% confidence interval for the proportion of adults who rated the economy as excellent/good. check conditions. b) does your confidence interval provide evidence to support the claim? c) what is the significance level of the test in b? explain.

a) The 99% confidence interval is given by (0.198;0.242).

b) Based on the p value obtained and using the significance level assumed we have so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.

c)

Step-by-step explanation:

Data given and notation  

n=2362 represent the random sample taken

X represent the people who says that  they would watch one of the television shows.

estimated proportion of people rated as Excellent/Good economic conditions.

is the value that we want to test

represent the significance level  

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 24% of people are rated with good economic conditions:  

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statistic, 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 .

Part a: Test the hypothesis

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

np = 2362x0.22=519.64>10 and n(1-p)=2364*(1-0.22)=1843.92>10

Condition satisfied.

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

The confidence interval would be given by:

The critical value using and would be . Replacing the values given we have:

So the 99% confidence interval is given by (0.198;0.242).

Part b

Statistical decision  

P value method or p value approach . "This method consists on 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.  

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

Since is a bilateral test the p value would be:  

So based on the p value obtained and using the significance level assumed we have so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.

Part c

The confidence level assumed was 99%, so then the signficance is given by

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step-by-step explanation:

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