Question

Crime concerns in China. A 2013 poll found that 24.2% of Chinese adults see crime as a very big problem, and the standard error for this estimate, which can reasonably be modeled using a normal distribution, is SE = 1.3%. Suppose an issue will get special attention from the Chinese government if more than 1-in-5 Chinese adults express concern on an issue.

1. Choose words from the dropdown choices to construct hypotheses regarding whether or not crime should receive special attention by the Chinese government according to the 1-in-5 guideline. Before making your choices consider the appropriateness of using a one-sided or two-sided test for this exercise. That is, for this decision process, would we care about one or both directions?

H0:H0: The proportion of adults in China who see crime as a very big problem is  ? more than not more than different from not different from less than not less than   ? 20% 24.2% 1.3% . The observed difference  ? is is not  due to chance.

HA:HA: The proportion of adults in China who see crime as a very big problem is  ? more than not more than different from not different from less than not less than   ? 20% 24.2% 1.3% . The observed difference  ? is is not  due to chance.

2. Calculate a z-score using the observed percentage and the two model parameters. Round to four decimal places. z =

3. Use the normal model to calculate a p-value. Round to four decimal places. p =

4. Based on your p-value, should crime receive special attention from the Chinese government?

? Yes No  because we  ? should should not  reject the null hypothesis.

Answer 1

Solution:

Given: A 2013 poll found that 24.2% of Chinese adults see crime as a very big problem, and the standard error for this estimate, which can reasonably be modeled using a normal distribution, is SE = 1.3%.

that is: and

An issue will get special attention from the Chinese government if more than 1-in-5 Chinese adults express concern on an issue.

That is: an issue will get special attention from the Chinese government if: p > 1/5 = 0.2 = 20%

Part 1)

H₀: The proportion of adults in China who see crime as a very big problem is not more than 20% .  The observed difference is due to chance.

H_A: The proportion of adults in China who see crime as a very big problem is more than 20% .  The observed difference is not due to chance.

Part 2) Calculate a z-score using the observed percentage and the two model parameters.

Part 3) Use the normal model to calculate a p-value.

p-value = P( Z > z test statistic value)

p-value = P( Z > 3.2308)

p-value = 1 - P( Z < 3.2308)

Use following Excel command:

=1-NORM.S.DIST(z , cumulative)

=1-NORM.S.DIST(3.2308,TRUE)

=0.0006

Thus p-value = 0.0006

Part 4) Based on your p-value, should crime receive special attention from the Chinese government?

Since p-value = 0.0006 < 0.05 level of significance , we reject null hypothesis H0.

Thus answer is:

Yes. because we should  reject the null hypothesis.