The lab manual says that repeated measurements will vary according to a Normal distribution with standard deviation o = 0.15. (This standard deviation shows how precise the measurement process is.) The mean µ of the distribution of measurements is the true specific gravity. (a) The lab manual asks for a 95% confidence interval for the true specific gravity. Your friend doesn't know how to do this. Do it for her. (b) Now explain to your friend in simple language what "95% confidence" means. (c) What critical value from the Normal table would you use if you wanted 80% confidence instead of 95% confidence? Would the 80% confidence interval be wider or narrower than your 95% confidence from(a)? (Do not actually compute the 80% confidence interval.) (d) The lab manual also asks whether the data show convincingly that the true specific gravity is less than 3.9. State the null and alternative hypotheses used to answer this question. Then, calculate the test statistic, and find its P-value.

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The lab manual says that repeated measurements will vary according to a
Normal distribution with standard deviation o = 0.15. (This standard deviation
shows how precise the measurement process is.) The mean µ of the distribution
of measurements is the true specific gravity.
(a) The lab manual asks for a 95% confidence interval for the true specific
gravity. Your friend doesn't know how to do this. Do it for her.
(b) Now explain to your friend in simple language what “95% confidence"
means.
(c) What critical value from the Normal table would you use if you wanted
80% confidence instead of 95% confidence? Would the 80% confidence interval
be wider or narrower than your 95% confidence from(a)? (Do not actually
compute the 80% confidence interval.)
(d) The lab manual also asks whether the data show convincingly that the
true specific gravity is less than 3.9. State the null and alternative hypotheses
used to answer this question. Then, calculate the test statistic, and find its
P-value.
Transcribed Image Text:The lab manual says that repeated measurements will vary according to a Normal distribution with standard deviation o = 0.15. (This standard deviation shows how precise the measurement process is.) The mean µ of the distribution of measurements is the true specific gravity. (a) The lab manual asks for a 95% confidence interval for the true specific gravity. Your friend doesn't know how to do this. Do it for her. (b) Now explain to your friend in simple language what “95% confidence" means. (c) What critical value from the Normal table would you use if you wanted 80% confidence instead of 95% confidence? Would the 80% confidence interval be wider or narrower than your 95% confidence from(a)? (Do not actually compute the 80% confidence interval.) (d) The lab manual also asks whether the data show convincingly that the true specific gravity is less than 3.9. State the null and alternative hypotheses used to answer this question. Then, calculate the test statistic, and find its P-value.
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