University of California Los Angeles Statistics Exercises Paper

The five questions in this homework all draw on the following information.

In early 2019, the Pew Research Center asked 6637 randomly selected adult Americans a series of questions about race in the United States. One question asked:

Would you say President Trump has . . .
1 Made progress toward improving race relations
2 Tried but failed to make progress toward improving race relations
3 Not addressed race relations
4 Made race relations worse

Respondents could answer with one of the four provided choices, or they could refuse to answer. The results for this question are:

1. At the bottom of the table, it says ±$\pm$0.031 95% MoE. Which of the following is the best interpretation of this table note?

Select one:

a. 95% of all samples will have figures similar to those given in the Prop. column

b. We are 95% confident that the figures given in the Prop. column are within .031 of the true population figures.

c. We are 95% confident that the answers in the Prop. column are correct.

d. 0.031 is 95% of the total amount of error in our study

2.The figures given in the Prop. column are correct for these data. Why do we need to take a confidence interval (or add a margin of error)?

Select one:

a. We are trying to guess what the figures are in the whole population.

b. The confidence allow us to claim a high level of confidence (95%) that we got the answer correct.

c. If we take smaller samples from this sample, we will get proportions like these 95% of the time.

d. We take a margin of error to guard against bias.

3.The researchers created an overall margin of error for the table. But it is more appropriate to take a margin of error for each response category. With the category ‘made progress’, we would estimate the 95% confidence interval (margin of error) as follows.

The margin of error can be calculated as: 1.96(????)$1.96\left(SE\right)$.

The standard error (SE) is estimated as: ??????????=.13?.87854???????=.1131103??????=.115$\sqrt{\frac{pq}{n}}=\sqrt{\frac{.13?.87}{854}}=\sqrt{\frac{.1131}{103}}=.115$

So the confidence interval is: .13±1.96(.0115)=.023$.13\pm 1.96\left(.0115\right)=.023$

I am 95% confident that the true population proportion saying ‘made progress’ is within .023 of .13.

Calculate the 95% margin of error for the category ‘Tried but failed’. What is your margin of error (round to 3 decimal places)?

Answer:

4.Another researcher points out that surveys of this sort tend to over represent students and white collar workers because they generally have more flexible schedules. This means our results might be biased. How can we address this problem using inferential statistics?

Select one:

a. We should eliminate the biased cases.

b. We should increase our confidence level to 99%.

c. We should decrease our confidence level to 90%.

d. We can’t use inferential statistics to deal with bias.

5.Calculate a 90% confidence interval for ‘made worse’ and then write a short paragraph describing results in this category and commenting on how it can be generalized to the population.