1. State the null and research hypotheses 2. Provide the Z(critical), T(critical

Question

1. State the null and research hypotheses
2. Provide the Z(critical), T(critical), or 2(critical) score corresponding to the thresh- old for your test
3. Provide your test statistic
4. Provide your decision about statistical significance
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.

1. A random sample of 250 persons yields a sample mean of 110 and a sample standard deviation of 10. Construct three different confidence intervals to estimate the popu- lation mean, using 95%, 99%, and 99.9% levels of confidence. What happens to the interval width as the confidence level increases? Why?

Explanation / Answer

N = 250 persons

sample mean xbar = 110

sample standard deviation s = 10

95% confidennce level: Z - value = +-1.96

so 95% confidennce level for population mean

= xbar +- 1.96 * s/ n = 110 +- 1.96 * 10/ 250

= (108.76, 111.24)

99% confidennce level: Z - value = +-2.575

so 99% confidennce level for population mean

= xbar +- 2.575 * s/ n = 110 +- 2.575 * 10/ 250

= (108.37, 111.73)

99.9% confidennce level: Z - value = +-3.29

so 95% confidennce level for population mean

= xbar +- 1.96 * s/ n = 110 +- 3.29 * 10/ 250

= (107.92, 112.08)

Width of confidence interval increases with increase in confidence level. It is because of increase in number of eligible values in confidence interval.

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