Statistical significance

A researcher collected ten questions in a survey about minority rights. 3000 randomly selected people living in California participated in the survey. She created a score of support for minority rights. Negative values mean opposition to minority rights; positive values indicate that the opinions are in favor of it. The researcher wants to know if the population’s average opinion in California supports minority rights. Due to privacy reasons, the researcher only had access to some sample summary statistics, such as the average, standard deviation, etc.

(a) Suppose that the researcher is informed that the sample avarage is xbar =4 and the sample variance is ˆσ2 = 4. Can she infer, with statistical significance, that the average opinion in the population in California is not neutral? Select a significance level and answer this question based on your selection.

(b) Suppose now that two mistakes occured. The company collecting the data changed places where some zeros should go when they sent the report to the researcher.

They called the researcher and said the sample size was actually 30, not 3000, and the vari- ance 400, not 4. Using a normal approximation for the sampling distribution of the mean, given this new information about the variance and the sample size, and using the same signif- icance level you selected in the previous item, can she conclude that the opinion is statistically significant not neutral? Using your own words, explains why the result changed or did not change.