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In order to compare the sample I collected (the household sizes from my neighborhood) to the city statistics, calculate the mean of the sample....
In order to compare the sample I collected (the household sizes from my neighborhood) to the city statistics, calculate the mean of the sample. (Round it to 1 decimal place.)
Because a sample should be compared to a population of samples, we need to turn the original household sizes from the city into a sampling distribution, which is composed of all the possible samples drawn from the whole city population of households. In order to position my sample on that sampling distribution, we need to know the standard deviation of the sampling distribution, which is also commonly called standard error (SE). Calculate SE from the city population statistics provided in the research scenario: mean (μ) = 3.1, SD (σ) = 1.6, along with the sample size N = 16. (Round it to 1 decimal place)
Now we need to locate our sample mean on the sampling distribution and see if it falls into an extreme (significance) area. If so, we would be able to reject the null hypothesis and say that the household sizes in my neighborhood are indeed significantly different from the city population of households. To figure out the position of our sample mean on the sampling distribution, calculate the Z statistic for our sample. (Report all decimal places if any.)
The result regarding significance only tells us whether the difference between the two populations being compared is statistically significant, but it does not tell us how big the potential difference is. Calculate the standardized effect size for this test, using the information provided in the research scenario and the answers from previous questions. (Round the answer to 2 decimal places.)
