1. Report the following results with the correct number of significant figures:
a. (1678.2 ± 230.4) g mL-1
b. (0.92356 ± 0.001178) kg m2
c. (2.173 ± 0.245)×10-10 m
d. (842.2 ± 5.761) m2 g-1
e. (223.58 ± 1.12) M
f. (1.26357 ± 0.2176) × 10-3 m
g. (842.2 ± 61.7) m2 g-1
Apply the rules for writing significant figures once you know the uncertainty. Use the same rules to report the results of all other exercises in the rest of this assignment!
2. The mass of a sample is measured multiple times using a balance with resolution 0.01 g resulting in dataset1 in the file. Provide an estimate of the same weight and define the 95% confidence interval.
Use the sample mean and the normal distribution commands to establish the confidence interval.
3. The mass of a sample is measured multiple times using a balance resulting in dataset1 in the file. Provide an estimate of the same weight and define the 95% confidence interval.
Consider here that you have no information on the standard deviation of mass values: even if the numbers are the same you have less information than in exercise (2). Choose the correct distribution to establish the 95% confidence interval.
4. Replicate measurements of the rate of hydrolysis of a reactant, yield the half-life values in dataset2. Provide a point estimate of the half-life of the reactant and define a 99% confidence interval.
Use the sample mean and the correct distribution to establish the confidence interval.
5. The carbohydrate content of glycoproteins is determined in replicate analyses using an analytical method. The content in g of carbohydrate per 100 g of protein obtained experimentally for two proteins is reported in dataset3. Do the two proteins differ in carbohydrate content at the 5% significance level? Assume that both populations have the same variance.
Use a two-sample test to answer this question.
6. In order to determine if a batch of paracetamol tablets meets standard specs, a random sample of ten tablets is quantitatively analyzed using HPLC methods to determine the amount of paracetamol resulting in dataset4. It is known that the concentration is normally distributed with standard deviation = 2. If the specifications state that the mean content should be 100 mg, does the batch conform to specs at the 5% significance level?
Hint: ask whether the mean over 10 measurements is within the 95% confidence interval for the means of 10 tablets of the proposed true population, with mean 100 and stedev 2.
7. The concentration of an atmospheric pollutant is measured at 8 different environmental stations across Dublin, before and after introducing new emission regulations for automobiles, yielding the concentrations in dataset5. Establish whether the regulations had a significant effect on pollutant concentrations at the 1% significance level.
Use the correct two-sample test to answer this question.
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