The average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years. A simple random sample of 100 residents is to be selected, and the sample mean age of these residents is to be computed.

The probability that the average age of the 100 residents selected is more than 70 years is  …

[Hint: first consider the sample standardised z-statistic]

In a large population of college-educated adults, the mean IQ is 118 with standard deviation 20. Suppose 100 adults from this population are randomly selected for a market research campaign.

What is the standardised score for a particular sample of 100 that gave a sample mean IQ of 120?

A simple random sample of 1000 American adults found that the average number of hours spent watching television during a typical week was 13.8. A simple random sample of 500 Canadians yielded an average of 12.5 hours per week of television viewing. Assume that the American and Canadian distributions for weekly television viewing times have the same standard deviations. The sampling variability associated with the sample means (described above) is

Parts being manufactured at a plant are supposed to weigh 40 grams. Suppose the distribution of weights has a Normal distribution with mean 40 grams and a standard deviation 2 grams. Quality control inspectors randomly select 16 parts, weigh each, and then compute the sample average weight for the 16 parts.

The sampling distribution of the sample mean

Suppose you interview 10 randomly selected workers and ask how many miles they commute to work. You'll compute the sample mean commute distance. Now imagine repeating the survey many, many times, each time recording a different sample mean commute distance. In the long run, a histogram of these sample means represents

For which of the following situations would the Central Limit Theorem for Sample Means NOT apply?

The law of large numbers states that as the number of observations drawn at random from a population with finite mean μ increases, the mean of the observed values

The central limit theorem says that when a simple random sample of size n is drawn from any population with mean μ and standard deviation σ, then when n is sufficiently large

Select ALL correct answers

Which of the following statements is correct about a parameter or a statistic associated with repeated random samples of the same size from the same population?

Eggs that are contaminated with salmonella can cause food poisoning among consumers. A large egg producer takes an SRS of 200 eggs from all the eggs shipped in one day. The laboratory reports that 11 of these eggs had salmonella contamination. Unknown to the producer, 0.2% (two-tenths of one percent) of all eggs shipped had salmonella. In this situation