Week 8 Notes

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Statistics

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Feb 20, 2024

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Topics Notes M14 M15 Is there evidence that Kiwi eggs have changed in size? A sample of 16 eggs yielded an average egg weight of 440 grams with a standard deviation of 20 grams. 1. State the null and alternative hypotheses. Is this a left tail, right tail, or two tail test? Are the guidelines met? H0 : μ = 450 HA : μ = 450 ̸ Two-tailed test. Yes, since the data come from a normally distributed population. 2. Calculate the test statistic to three (3) decimal places. t = (440 – 450)/(20/√16) = −2 3a. Compute the critical value(s) to three (3) decimal places using α = 0.10. CVs =T.INV(0.05, 15), T.INV(1 - 0.05,15) = ±1.753 You can use the two-tailed t-distribution commands as well. The answers then are ± =T.INV.2T(0.10, 15). 3b. Compute the p-value to four (4) decimal places. p-value =T.DIST(-2,15,TRUE)×2 = 0.0639 Again, you can use the two-tailed t-distribution commands as well by using =T.DIST.2T(2, 15) 4. State the conclusion of the test using both the critical value method and the p-value method by filling in the blanks with the appropriate terms such as can, cannot, do, do not, less than, greater than, etc. Because the test statistic is outside the critical value(s), we can reject the null hypothesis. Because the p-value is less than our α of 0.01, we can reject the null hypothesis. 5. Interpret your results We do have sufficient evidence to say that the average mass of kiwi eggs is ! = 450 grams. - Intervals depend on the sample and are random. - Say “xx% confident that the interval contains the mean/proportion.” - Do not say “xx% probability that the mean/proportion is in the interval.” - Intervals have the form: statistic plus or minus ever-so-many standard errors. - The statistic is x or ˆp. ̄ - The standard error is s/√n or pˆp(1 − ˆp)/n. - Ever-so-many depends on the level of confidence, 100(1 − α)% and is the value of the normal distribution (for proportions) or t- distribution (for means) that puts α/2 in the tail. When we don’t know p, so what do we do? - Use an estimate from previous studies or knowledge. - Use p = 0.5 to get the largest sample size needed to work for all

values of p ALWAYS ROUND n UP Summary

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