Practice Quiz 3 covering Chapter 11        Name: __________________________

Instructions: Answer each question, and when required explain your answer. Your explanation must be clear and complete. You may refer to your book, your notes and your homework papers. Calculators are allowed.

[1] Sketch two normal distributions using the same x-axis. Label them distribution I and distribution II, such that distribution I has a larger mean but a smaller standard distribution.

[2] Using Table 11.3 on p. 709, determine what percentage of a normally distributed population has z values in the range from -1.5 to 0.5.

[3] Assume IQ scores for adults are normally distributed with a mean of 100 and a standard deviation of 15.
(a) What percentage of adults have IQ scores in the range 70 to 130? Explain how you obtain your answer.

(b) What IQ score must one have in order for 90.32% of the population to have that score or less? (Hint: use Table 11.3 on p. 709.)

[4] (a) Find the 95% confidence interval for a survey on taxes which used a sample size of 2500 and found a sample proportion of p^ = 10% in favor of higher taxes. Explain how you obtain your answer.

(b) What sample size n is needed in order for the sampling distribution for samples of that sample size to be approximately normally distributed, if the population proportion p is 10%? Explain how you obtain your answer.

(c) What sample size n is needed in order both for the sampling distribution to be approximately normal and for at least 95% of all possible samples of that sample size to have a sample proportion p^ in the range 10% plus or minus 2%, if the population proportion p is 10%? Explain how you obtain your answer.

[5] In reference to a news article (saying that a national survey of 1000 randomly chosen respondents has found that national sentiment on some topic is 89% plus or minus 2% in support of the issue), a colleague of yours mentions to you that journalists just don't understand that a sample of 1000 individuals chosen at random from a population of 100,000,000 is too small a sample to reliably "show" or "find" the feelings of that large mass. You decide (possibly against your better instincts) to explain to your colleague in what sense it is reliable, and how reliable it is. What do you say?