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STAT100 Elementary Statistics For Applications

1. To compare the effect of stress in the form of noise on the ability to perform a simple task, 70 subjects were divided into two groups. The first group of 30 subjects acted as a control, while the second group of 40 were the experimental group. Although each subject performed the task in the same control room, each of the experimental group subjects had to perform the task while loud rock music was played. The time to finish the task was recorded for each subject and the following summary was obtained:

Find a 99% confidence interval for the difference in mean completion times for these two groups.

2. Suppose you wish to estimate a population mean based on a random sample of observations, and prior experience suggests that σ  12.7. If you wish to estimate µ correct to within 1.6,with probability equal to 0.95, how many observations should be included in your sample?

3. A study conducted by the doctors of a particular hospital involved monitoring a random sample of 75 patients. The results showed that it took an average of 3 cc of tranquillizer, with a standard deviation of 0.2 cc, to put a patient to sleep before surgery.

a) Find a point estimate for population mean.
b) Construct a 95% confidence interval for the true mean amount of tranquillizer needed to put any patient to sleep.

4. A researcher wants to determine the proportion of elm trees in Windsor, Ontario, dying of Dutch elm disease. Past experiments, based on large sample sizes, have shown this proportion to be 0.3. What sample size does the researcher need in order to estimate this proportion to within 0.04 with 98% confidence?

5. In a random sample of 519 students, it was found that 285 were introverts.

a) Let p represent the proportion of all students who are introverts. Find a point estimate forp.