Z and T Statistics: Confidence Intervals and Significance Tests: A friend who hears that you are taking a statistics course asks for help with a specific chemistry lab report. She has made four independent measurements of the specific gravity of a compound. The results are : 4.48, 4.6, 4.33 and 4.57. You are willing to assume that the measurements are not biased. This means that the mean M of the distribution of measurement is the true specific gravity.
4.48
4.6
4.33
4.57
a) Calculate a 95% confidence interval for the true specific gravity for your friend. (Use Table T)
b) Explain to your friend what this means (Use Table T)
c) What must be true about your friend's measurements for your results in part (a) to be correct? (Use Table T)
d) You notice that the lab manual says that repeated measurements will vary according to a normal distribution with standard deviation 0=0.11. Redo the confidence interval of part (a) using this additional information. Explain why we expect the new interval to be shorter. (Use Table Z*)
e) What critical value from the table would you use for an 80% confidence interval? Without calculating that interval would you expect it to be wider or narrower that the 95% confidence interval? (Use Table Z*)
f) The lab manual also asks whether the data show convincingly that the true specific gravity is less than 4.5. State the null hypothesis used to answer this question. Then calculate the test statistic and find its P-value. Use the lab manual's value o=0.11 and calculate the p-value in detail. (Use Table Z*)
g) Explain to your friend what your p-value means. (Use Table Z*)
4.48
4.6
4.33
4.57
a) Calculate a 95% confidence interval for the true specific gravity for your friend. (Use Table T)
b) Explain to your friend what this means (Use Table T)
c) What must be true about your friend's measurements for your results in part (a) to be correct? (Use Table T)
d) You notice that the lab manual says that repeated measurements will vary according to a normal distribution with standard deviation 0=0.11. Redo the confidence interval of part (a) using this additional information. Explain why we expect the new interval to be shorter. (Use Table Z*)
e) What critical value from the table would you use for an 80% confidence interval? Without calculating that interval would you expect it to be wider or narrower that the 95% confidence interval? (Use Table Z*)
f) The lab manual also asks whether the data show convincingly that the true specific gravity is less than 4.5. State the null hypothesis used to answer this question. Then calculate the test statistic and find its P-value. Use the lab manual's value o=0.11 and calculate the p-value in detail. (Use Table Z*)
g) Explain to your friend what your p-value means. (Use Table Z*)
