invest_3ed.pdf

# X t probability calculator applet o specify 4 as the

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x t Probability Calculator applet: o Specify 4 as the degrees of freedom o Check the box next to the less than symbol and then entire .025 in the probability box and press Return. The t-value box should fill in. How does this critical value compare to the corresponding z * value for 95% confidence? t 4 * = z * = Comparison: (v) Repeat (u) for the sample size of n = 13. How do the t -critical values compare for these different sample sizes? Is this what you expected? Explain. (w) Repeat (v) for the sample size of n = 130. How does this value compare to the earlier t * and z * values? (x) Use the critical value from (w) to calculate a 95% confidence interval for the mean body temperature of a healthy adult based on our sample ( x = 98.249, s = 0.733). Is this interval consistent with your conclusion about the null hypothesis in (o)? Explain.

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Chance/Rossman, 2015 ISCAM III Investigation 2.5 163 Technology Detour One Sample t -procedures In R , you can use the t.test command with raw data (“x”) or iscamonesamplet with summary data > OR t.test(x, mu = P » µ alternative="two.sided", conf.level = .95) > iscamonesamplet(xbar=98.249, sd=.733, n =130, hypothesized = 98.6, alternative = "two.sided", conf.level = 95) where sd = sample standard deviation, s . In Minitab x Choose Stat > Basic Statistics > 1-Sample t . x Specify the column of data or use the pull-down menu for Summarized data and enter the sample size, mean, and standard deviation. x Check the box to perform the hypothesis test and enter the hypothesized value of P . x Under Options specify the direction of the alternative. (Use the two-sided option to get a confidence interval.) x Press OK twice. In Theory-Based Inference applet x Select One mean from the Scenario pull-down menu x You can check Paste data to copy and paste in the raw data, or type in the sample size, mean, and standard deviation. Press Calculate . x Check the box for Test of significance and enter the hypothesized value of P and set the direction of the alternative. Press Calculate . x Check the box for Confidence interval , enter the confidence level and press Calculate CI . (y) Verify your by-hand calculations with technology and summarize the conclusions you would draw from this study (both from the p-value and the confidence interval, including the population you are willing to generalize to). Also include interpretations, in context, of your p-value and your confidence level.
Chance/Rossman, 2015 ISCAM III Investigation 2.5 164 Study Conclusions The sample data provide very strong evidence that the mean body temperature of healthy adults is not 98.6 degrees ( t = ± 5.46, two-sided p-value < 0.001). This indicates there is less than a 0.1% chance of obtaining a sample mean as far from 98.6 as 98.249 in a random sample of 130 healthy adults from a population with mean body temperature of 98.6 0 F. A 95% confidence interval for the population mean body temperature is (98.122, 98.376), so we can be 95% confident that the population mean body temperature among healthy adults is between 98.122 and 98.376 degrees. This interval is entirely less than 98.6, consistent with our having found very strong evidence to reject 98.6 as a plausible value for the population mean.

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