1. Suppose the estimate of a proportion of a normal population is to be within 0.05 using the 95% confidence level. How large a sample is required if:
a. It is known from previous studies that p = 0.3?
b. There is no prior knowledge of p?
2. Each of the following is a large-sample confidence interval for μ, the mean resonance frequency (HZ) for all tennis rackets of a certain type. (114.4, 115.6), (114.1, 115.9)
a. What is the value of the sample mean resonance frequency?
b. Both intervals were calculated from the same data. The confidence level of one of these intervals is 90% and the other is 99%. Which of these intervals has the 99% confidence level, and why?
3. Determine the t-critical value for a two-sided confidence interval in each of the following situations.
a. Confidence level = 95%, df = 15
b. Confidence level = 99%, n = 5.
c. Confidence level = 95%, n = 15
d. Significance level = 0.01, df = 37
4. A study of the ability of individuals to walk in a straight line (“Can We Really Walk Straight?”, Amer. J. of Physical Anthro., 1992:19-27) reported the accompanying data on cadence (strides per second) for a sample of 20 randomly selected individuals.
0.95 0.82 0.92 0.95 0.93 0.86 1.00 0.92 0.85 0.81 0.78 0.93 1.05 0.93 1.06 0.96 0.81 0.96 0.92 0.93
Construct a 95% confidence interval for the true mean cadence.
5. An Aspirin manufacturer fills bottles by weight rather than by count. Since each bottle should contain 100 tablets, the average weight per tablet should be 5 grains. Each of 100 tablets taken from a large lot is weighed, resulting in a sample average weight per tablet of 4.87 grains and a sample standard deviation of 0.35 grain. Does this information provide strong evidence for concluding that the company is not filling its bottles as advertised? Test H0: μ = 5 against HA: μ < 5 at the 0.01 level of significance