Question

5. People's Critical Comment: the street-stall economy should be heated, but cannot be "feverish".

After the outbreak of COVID-19, some local governments have supported the street-stall economy, reviving the local economies, and making a living way for people whose income has decreased because of COVID-19 pandemic. However, if the scale of street-stall economy is too large, it could negatively influence the social and market order; government inappropriate encouragement may lead to another kind of unfairness. What should stores do if street stalls are encouraged? What should pedestrian do if street vendors are encouraged to do business on the roadside and walkway? Encouraging street-stall economy could result in more new problems, possibly posing a bigger challenge to the administration and violating public interest, which is likely to cause market entities to lose the balance of interest. In this way, it could betray the original intention of the policy which is to support the people's livelihood with street-stall economy. “Tolerance” means that government should have a more precise evaluation of public interest, not only considering the livelihood of street vendors, but also considering the stores; not only opening more business space for low-income people, but also protecting the basic order of public transport, as well as controlling noise pollution, ensuring food security etc. There are too many aspects that governments should consider. Tolerance to street stalls is the only way that can keep the original intention of the policy to the greatest extent, but the active motivation and encouragement from governments may lead to the new unfairness and disorder, which could diverge from the original intention of the street-stall economy policy, making this policy losing its special value.

Please come up with a question about confidence interval estimation about difference of two population means (independent sample) in this background. The students with the ending number of 0-3 in their student numbers should use the Z-test statistics, and the sample sizes of the two groups are 8 and 9 respectively, and the confidence level is 99%.

The students with the ending number of 4-6 should use pooled-variance t test statistic, and the sample sizes of the two groups are 7 and 8 respectively, and the confidence level is 95%.

The students with the ending number of 7-9 in student number should use t test statistic, and the sample sizes of the two groups are 6 and 7 respectively, and the confidence level is 90%. (20 points)

Answer 1

We want to check whether the government policy effects the business of stores against the street-stalls.

Let the average sale in a day for stores = before the implementation of the policy

and the average sales in a day for stores = after the implementation of the policy

1st part

The confidence interval with Z statistic is

Given and and confidence limit is 99%

So the above confidence interval is reduced to

2nd part

If the policy does not have any effect then or

Alternatively, there will be ; which will show that there is an effect of the policy.

According to the problem, the sample size came from a normal population with population mean of and respectively

Since all population parameters are unknown, we will use t statistic

where t calculated

which follows t with df

with 13 df

3rd part

Given and

The confidence level is given by with 90% confidence

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