random sample of n = 100 measurements of calcium concentration (mg/l) of water is taken from a freshwater lake. A 95% confidence interval for the (population) mean calcium concentration is subsequently found to be 0.49 mg/l to 0.82 mg/l. 1. (a) Would a 90% confidence interval from the same sample be longer or shorter? Explain you response. 2. (b) Whichoneofthefollowingtwostatementsgivesacorrectinterpretationoftheconfidence interval? There is a 95% chance that µ is between 0.49 and 0.82 mg/l. If a new random sample of n = 100 measurements is taken from the lake and the i. ii. 95% confidence interval for µ is computed, and this process is repeated many times, then approximately 95% of the resulting confidence intervals would contain the true (unknown) value of µu. 95% of the estimates from future studies will fall inside the interval 0.49 to 0.82 mg/l. 95% of the n = 100 measures in this data set fall inside the interval 0.49 to 0.82 mg/l. iii. iv.

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random sample of n = 100 measurements of calcium concentration (mg/l) of water is taken from a
freshwater lake. A 95% confidence interval for the (population) mean calcium concentration is
subsequently found to be 0.49 mg/l to 0.82 mg/l.
1. (a) Would a 90% confidence interval from the same sample be longer or shorter? Explain your
response.
2. (b) Whichoneofthefollowingtwostatementsgivesacorrectinterpretationoftheconfidence
interval?
There is a 95% chance that µ is between 0.49 and 0.82 mg/l.
If a new random sample ofn = 100 measurements is taken from the lake and the
i.
ii.
95% confidence interval for u is computed, and this process is repeated many times,
then approximately 95% of the resulting confidence intervals would contain the true
(unknown) value of p.
95% of the estimates from future studies will fall inside the interval 0.49 to 0.82 mg/l.
95% of the n = 100 measures in this data set fall inside the interval 0.49 to 0.82 mg/l.
ii.
iv.
3. (c) Pick one of the three incorrect statements you did not choose in (b) and explain why it is
incorrect.
Transcribed Image Text:random sample of n = 100 measurements of calcium concentration (mg/l) of water is taken from a freshwater lake. A 95% confidence interval for the (population) mean calcium concentration is subsequently found to be 0.49 mg/l to 0.82 mg/l. 1. (a) Would a 90% confidence interval from the same sample be longer or shorter? Explain your response. 2. (b) Whichoneofthefollowingtwostatementsgivesacorrectinterpretationoftheconfidence interval? There is a 95% chance that µ is between 0.49 and 0.82 mg/l. If a new random sample ofn = 100 measurements is taken from the lake and the i. ii. 95% confidence interval for u is computed, and this process is repeated many times, then approximately 95% of the resulting confidence intervals would contain the true (unknown) value of p. 95% of the estimates from future studies will fall inside the interval 0.49 to 0.82 mg/l. 95% of the n = 100 measures in this data set fall inside the interval 0.49 to 0.82 mg/l. ii. iv. 3. (c) Pick one of the three incorrect statements you did not choose in (b) and explain why it is incorrect.
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