Office: 231 Ketter Hall Email: qw6@buffalo.edu Instructor Qian Wang Phone: (716)

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Office: 231 Ketter Hall Email: qw6@buffalo.edu Instructor Qian Wang Phone: (716) 645-4365 un) M T W TILE 1.00-11.50AM. Ketter 231: TAs O: to be posted Homework # 1:Sampling and Descriptive Statistics Due date: Before the class starts on September 5 (Wed), 2018 Three.preblems in total related to Chapter 1 of the textbook Preblem 1 1: Suppose you are a pollster who is responsible for sampling 100 registered voter in City of Butilo to collect responses regarding which candidate they support for mayor Answer the following questions: (1) Four sampling strategies are proposed as below. Explain what sampling method each strategy belongs to (e.g, simple random sampling, sampling of convenience, or stratified random them is good, than others) sampling). Which strategy would be the best? Why? (Note: if you think none of please propose your own sampling strategy and explain why it is better Sampling strategy I: arrange the social security numbers of all the registered voters in the city according to an ascending order, and then select the first 100 registered voters in the list. Sampling strategy 2: number all the registered voters in the city, and then use a random number generator provided by Excel to pick 100 number and the associatesd voters Sampling strategy 3: group the registered voters by gender, and then use a random number generator to sample 20 females and 80 males separately Sampling strategy 4: ask questions to the first 100 registered voters you encounter on the UB campus. eventually collect responses from a random sample of 100 registered voters, and 40 of them support candidate NOBODY. Are the following statements true or false? Why? a. The proportion of registered voters in City of Buffalo who support candidate NOBODY is 0.4 The proportion of registered voters in City of Buffalo who support candidate NOBODY is likely to be close to 0.4, but not equal to 0.4. b. (3) Suppose you reach out to the same group of voters and collect their responses again after a major televised debate (scheduled after the first survey). Among the same group of 100 voters, 45 state that they support candidate NOBODY. Can you make a conclusion that the televised debate does help NOBODY to gain more support? Explain why (4) Which outcome represents stronger evidence that the televised debate helps candidate NOBODY: finding 45 supporters in the sample, of finding 50 supporters in the sample? 1/3

Explanation / Answer

1) Stratified sampling is good for this case but if you see the sex ratio then there are more women than men in the population. So, if you take 20 women and 80 men then this will not give you a good result.

2) Both are false.

a) For the first one, we have the estimate of proportion is 0.4. That doesn't mean that the proportion is exactly 0.4. It may be or may not be.

b) For the second case, we can say that the proportion will be close to 0.4, but it can't say that it will not be 0.4, it may be or may not be.

3) In this case, if you perform a one sample proportion z test to test the null hypothesis that proportion is 0.4 against the alternative that proportion is greater than 0.4, you will have the resultant p-value is 0.15, which leads to conclude at 5% level of significance that we don't have enough evidence to say that the proportion is greater than 0.4. So, it can't support that the television debate does help NOBODY to gain more support.

4) When we have 50 supporters for NOBODY, then it is statistically significant to conclude that the proportion is greater than 0.4 using the same statistical test used before. Here the p-value is 0.02. So, finding 50 supporters in the sample is stronger evidence.

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