In: Math
Answer the questions below using the appropriate statistical technique. For questions involving the use of hypothesis testing, you must:
1. State the null and research hypotheses
2. Provide the Z(critical), T(critical), or χ 2 (critical) score corresponding to the α threshold for your test
3. Provide your test statistic
4. Provide your decision about statistical significance
A random sample of 350 persons yields a sample mean of 105 and a sample standard deviation of 10. Construct three different confidence intervals to estimate the population mean, using 95%, 99%, and 99.9% levels of confidence. What happens to the interval width as the confidence level increases? Why?
You must also substantively interpret the results of your test (but keep it short). That is, don’t just focus on whether or not a test is statistically significant, but also briefly comment on what the result actually means. You may find it helpful to proceed using the five-step model, but this is optional. Be sure to select a test that is appropriate given the question and decide whether the question calls for a one-tailed or two-tailed test. As well, do not round until the final step of your calculations.