Exam 9: Statistical Inference and Sampling Distributions

A video rental store wants to know what proportion of its customers are under 21 years old. A simple random sample of 500 customers is taken, and 350 of them are under 21. Assume that the true population proportion of customers aged under 21 is 0.68. If another simple random sample of size 500 is taken, what is the probability that more than 70% of customers are under 21 years old?

The central limit theorem states that if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean $\bar { X }$ :

Which of the following are the two most important types of data?

If all possible samples of size n are drawn from an infinite population with mean ? and standard deviation ?, then the standard error of the sample mean is inversely proportional to:

A sample of size 50 is to be taken from an infinite population whose mean and standard deviation are 52 and 20, respectively. The probability that the sample mean will be larger than 49 is:

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a standard deviation of 10 centimetres. Use this information to answer the following question(s). What is the probability that a randomly selected woman is shorter than 162 centimetres?

Consider an infinite population with a mean of 160 and a standard deviation of 25. A random sample of size 64 is taken from this population. The standard deviation of the sample mean equals:

The heights of 9-year-old children are normally distributed, with a mean of 123 cm and a standard deviation of 10 cm. a. Find the probability that one randomly selected 9-year-old child is taller than 125 cm. b. Find the probability that three randomly selected 9-year-old children are taller than 125 cm. c. Find the probability that the mean height of three randomly selected 9-year-old children is greater than 125 cm.

A researcher conducted a survey on a university campus for a sample of 64 third-year students and reported that third-year students read an average of 3.12 books in the prior academic semester, with a standard deviation of 2.15 books. Determine the probability that the sample mean is: a. less than 3.45. b. between 3.38 and 3.58. c. above 2.94.

The finite population correction factor should not be used when:

A sample of 50 observations is drawn at random from a normal population whose mean and standard deviation are 75 and 6, respectively. a. What does the central limit theorem say about the sampling distribution of the sample mean? Why? b. Find the mean and standard error of the sampling distribution of the sample mean. c. Find P( $\bar { X }$ > 73). d. Find P( $\bar { X }$ < 74).

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a variance of 100 centimetres2. A random sample of five women is selected. What is the probability that the sample mean is greater than 162 centimetres?

A sample of size 400 is drawn from a population whose mean and variance are 5000 and 10 000, respectively. Find the following probabilities. a. P( $\bar { X }$ < 4,990). b. P(4995 < $\bar { X }$ < 5010). c. P( $\bar { X }$ = 5000).

If the daily demand for boxes of mineral water at a supermarket is normally distributed with a mean of 47.6 boxes and a standard deviation of 5.8 boxes, what is the probability that the average demand for a sample of 10 supermarkets will be less than 50 boxes in a given day?

When a great many simple random samples of size n are drawn from a population that is normally distributed, the sampling distribution of the sample means will be normal, regardless of sample size n.

Which of the following best describes numerical statistical variables?

The sampling distribution of the sample proportion has mean p and variance pq/n.

If all possible samples of size n are drawn from a population, the probability distribution of the sample mean $\bar { X }$ is called the:

A sample of size 70 is selected at random from a finite population. If the finite population correction factor is 0.808, the population size (rounded to the nearest integer) must be 200.

Random samples of size 64 are taken from an infinite population whose mean is 160 and standard deviation is 32. The mean and standard error of the sample mean, respectively, are: