Answer :
Answer:
Step-by-step explanation:
Hello!
The claim is that the Chinese government will get special attention to an issue if more than 1-in-5 Chinese adults express concern on an issue.
The study variable is X: the proportion of Chinese adults that see crime as a very big problem.
The parameter of interest is the population proportion of Chinese adults that see crime as a very big problem.
If this proportion is greater than 1/5= 0.20 then the government will get special attention to crime, so the hypotheses are:
1.
H₀: p ≤ 0.2
H₁: p > 0.2
2.
Using the information that the sample proportion is p'= 0.233 and the standard error for the approximation to a normal distribution SE= 0.014, the statistic value is
[tex]Z_{H_0}= \frac{0.233-0.2}{0.014} = 2.3571[/tex]
3.
A little reminder: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).
This hypothesis test is one-tailed to the right, the p-value has the same direction as the test so to calculate it you have to do the following calculations:
P(Z ≥ 2.3571)= 1 - P(Z < 2.3571)= 1 - 0.991= 0.009
4.
The decision rule using the p-value is the following:
If p-value ≤ α, then you reject the null hypothesis.
If the p-value > α, then you do not reject the null hypothesis.
There is no significant level specified, but if for example, you use a level of α: 0.05, since the p-value is less, then the decision is to reject the null hypothesis.
Using a significance level of 5% you can conclude that more than 1 out of 5 adults consider crime as a very big problem and the Chinese government should give special attention to crime.
I hope it helps!
In this exercise we have to use probability knowledge to explain the hypotheses that are being addressed, so we find that:
1) [tex]H_0\leq 0.2\leq H_1[/tex]
2) [tex]2.3571[/tex]
3) [tex]0.009[/tex]
4) Using a significance level of 5% we can conclude that more than 1 out of 5 adults consider crime as a very big problem.
The claim is that the Chinese government will get special attention to an issue if more than 1-in-5 Chinese adults express concern on an issue. The parameter of interest is the population proportion of Chinese adults that see crime as a very big problem. If this proportion is greater than 1/5= 0.20 then the government will get special attention to crime, so the hypotheses are:
1) [tex]H_0: p \leq 0.2\\H_1: p > 0.2\\H_0\leq 0.2\leq H_1[/tex]
2) Using the information that the sample proportion is p'= 0.233 and the standard error for the approximation to a normal distribution SE= 0.014, the statistic value is
[tex]Z_{H}_0= \frac{0.233-0.2}{0.014} = 2.3571[/tex]
3) The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis. This hypothesis test is one-tailed to the right, the p-value has the same direction as the test so to calculate it you have to do the following calculations:
[tex]P(Z \geq 2.3571)= 1 - P(Z < 2.3571)\\= 1 - 0.991\\= 0.009[/tex]
4) The decision rule using the p-value is the following:
- p-value ≤ α, then you reject the null hypothesis.
- p-value > α, then you do not reject the null hypothesis.
There is no significant level specified, but if for example, you use a level of α: 0.05, since the p-value is less, then the decision is to reject the null hypothesis. Using a significance level of 5% you can conclude that more than 1 out of 5 adults consider crime as a very big problem and the Chinese government should give special attention to crime.
See more about probability at brainly.com/question/795909