A random sample of 25 Indiana farms had a mean number of cattle per farm of 27 with a sample standard deviation of five. Assuming the population is normally distributed, what would be the 95% confidence interval for the number of cattle per farm?
How do I know this is supposed to be a 2 tail test?
It’s not a two tailed test (although you do need upper and lower critical values). They haven’t given you a hypothesized parameter value to make an inference about. Confidence intervals and hypothesis tests are related, but different statistical approaches to answering questions. All you need to do in this question is calculate a confidence interval. Hope this helps!
More bluntly: it’s a confidence interval, not an hypothesis test.
The confidence interval is a range of values where the real population mean could lie given a confidence level (say 95% confidence) with a given sample from that population. You got the mean and the standard deviation from that sample, so look at the mean as a center and the standard deviation as a measure of how much that mean can vary in both directions, upper and lower the mean, that is why you need 2 critical values which represent the confidence level (the higher the confidence, the higher the critical value, so higher probability that the real population mean lie inside the CI ).
So the CI is: 27 + 2.04 (5 / sqrt(25))… and 27 - 2.04 (5 / sqrt(25))…