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Stats Quiz - P-value was less than the α value we can...

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Matthew Francis STAT 221, Section 83 Essay Quiz 31 a) State: Do the data provide sufficient evidence that the mean rod diameter exceeds 8.20 mm? Formulate: Observational study. Perform one-sample t test on the mean. The parameter is the mean rod diameter, and the population is all the rods produced by that machine. H o : μ = 8.20mm versus H a : μ > 8.20mm where μ = the mean diameter of the rods from that machine. Set α = .05. Solve: The plot shape is relatively Normal, not strongly skewed and with no outliers. Conditions: Randomness and population diameters Normally distributed. Checks: SRS was conducted for randomness. Plot (above) reveals neither strong skewness nor outliers. Thus, Normality is assumed since t procedures are robust with respect to Normality provided there are no outliers or strong skewness. (x-bar) = 8.234mm. s = .025298mm. Test statistic: t = (x-bar) μ o = 8.234 – 8.20 = 5.205 df = n–1 = 15–1 = 14 s/( n^½) .025298/(15^½) P -value < 0.0005 (from Table C). Conclude: As the
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Unformatted text preview: P-value was less than the α value, we can conclude that the results are statistically significant and thus we can reject H o and assume H a . We have sufficient evidence to conclude that the mean diameter is significantly greater than 8.20mm. b) State: What is a 95% confidence interval estimate for the true mean diameter of the metal rods from this machine? Formulate: Observational study. Calculate a one sample t confidence interval for the true mean. The parameter is the true mean rod diameter, and the population is all metal rods from that machine. Use a level of confidence of 95%. Solve: See above for data plot and condition checks. (x-bar) = 8.234mm. s = .025298mm. df = n–1 = 15–1 = 14 t confidence interval: (x-bar) ± t * s / ( n^½) = 8.234 ± 2.145(.025298/[15^½]) = 8.234 ± 0.014 = (8.220, 8.248) Conclude: We are 95% confident that the true mean diameter of the metal rods produced by this machine is somewhere between 8.220mm and 8.248mm....
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