invest_3ed.pdf

# B the responses to two other survey questions are

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(b) The responses to two other survey questions are given below. Without calculating, would the p- values for each of these comparisons be larger or smaller to the p-value in (a)? US UK "How likely do you think it is that there will be a major terrorist attack in this country in the next twelve months?" 62% thought likely 64% thought likely "How much confidence do you have in the ability of the government to reduce the likelihood of a terrorist attack?" 72% greatly or somewhat confident 54% greatly or somewhat confident (c) The Harris Interactive website included the following statement: In theory, with probability samples of this size, one could say with 95 percent certainty that the results have a statistical precision of plus or minus 1.7 percentage points (in the US poll, 2 percentage points in the UK poll) of what they would be if the entire adult population had been polled with complete accuracy. Unfortunately, there are several other possible sources of error in all polls or surveys that are probably more serious than theoretical calculations of sampling error. They include refusals to be interviewed (non- response), question wording and question order, and weighting. It is impossible to quantify the errors that may result from these factors. This online sample is not a probability sample. - Where do the “1.7 percentage points” and “2 percentage points” figures come from? - Why do you think they state that this online sample is not a probability sample?

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Chance/Rossman, 2015 ISCAM III Example 3.2 247 Analysis (a) The response variable is categorical and binary. Suppose we define “success” as “not worrying much or at all about a terrorist attack in their country.” Then we can let S US S UK represent the difference in the population proportions that would respond that they don’t worry much or at all. H 0 : S US S UK = 0 (there is no difference in the population proportions) H a : S US S UK ≠ 0 (there is a difference) Note: We were not given a conjectured direction as to which country would have a higher population proportion. Because these polls were conducted separately in the two countries, the samples are independent. However, as discussed in (c), they are not true random samples, so we need to have some caution in generalizing these results to all adults over the age of 18 in the two countries. The sample sizes were large (over 900 successes and failures in each sample) so the normal distribution would be a reasonable model for the sampling distribution of the difference in sample proportions. Using this normal distribution model, we would expect the distribution of the difference in sample proportions to be centered at zero. Assuming that the null hypothesis of equal population proportions is true, our estimate of the standard deviation of this distribution is 1 1 0.433(1 0.433) 3378 2417 § · ± ² ¨ ¸ © ¹ = 0.0132 where 0.433 = (1520+991)/(3378+2417), the pooled estimate of the proportion of successes.
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