Exam 9: Statistical Inference and Sampling Distributions

The type of data being measured is one of the first key factors of determining the statistical methods that should be used.

Which of the following best describes the Central Limit Theorem?

The amount of time spent by Australian adults playing sports per day is normally distributed, with a mean of 4 hours and standard deviation of 1.25 hours. Find the probability that if four Australian adults are randomly selected, their average number of hours spent playing sport is more than 5 hours per day.

If it is known that the population proportion of car parks in a particular city that offer early discount fees is 25%, which of the following best describes the mean and standard deviation of the sampling distribution of the sample proportion of car parks that offer early discount fees for samples taken of size 30?

In order to estimate the mean salary for a population of 500 employees, the managing director of a certain company selected at random a sample of 40 employees. a. Would you use the finite population correction factor in calculating the standard error of the sample mean? Explain. b. If the population standard deviation is $800, compute the standard error both with and without using the finite population correction factor. c. What is the probability that the sample mean salary of the employees will be within ±$200 of the population mean salary?

The amount of time spent by Australian adults playing sports per day is normally distributed, with a mean of 4 hours and standard deviation of 1.25 hours. Use this information to answer the following question(s). Find the probability that a randomly selected Australian adult plays sport for more than 5 hours per day.

An infinite population has a mean of 100 and a standard deviation of 20. Suppose that the population is not normally distributed. What does the central limit theorem say about the sampling distribution of the mean if samples of size 64 are drawn at random from this population?

A sample of size n is selected at random from an infinite population. As n increases, which of the following statements is true?

The expected value of the sampling distribution of the sample mean $\bar { X }$ equals the population mean ?:

An infinite population has a mean of 120 and a standard deviation of 44. A sample of 100 observations is to be selected at random from the population. a. What is the expected value of the sample mean? b. What is the standard deviation of the sample mean? c. What is the shape of the sampling distribution of the sample mean? d. What does the sampling distribution of the sample mean show?

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a standard deviation of 10 centimetres. What is the probability that the mean height of a random sample of 30 women is smaller than 162 centimetres?

A normally distributed population with 200 elements has a mean of 60 and a standard deviation of 10. The probability that the mean of a sample of 25 elements taken from this population will be smaller than 56 is:

If a random variable X is not known to be normally distributed, has a mean of size 8 and a variance of size 1.5, describe the sampling distribution of the sample mean for samples of size 30.

Given an infinite population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations, taken at random from this population, exceeds 78 is:

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 375 of them are under 21. Assume that the true population proportion of customers aged under 21 is 0.68. What is the probability that the sample proportion will be within 0.03 of the true proportion of customers who are aged under 21?

A local newspaper sells an average of 2100 papers per day, with a standard deviation of 500 papers. Consider a sample of 60 days of operation. a. What is the shape of the sampling distribution of the sample mean number of papers sold per day? Why? b. Find the expected value and the standard error of the sample mean. c. What is the probability that the sample mean will be between 2000 and 2300 papers?

A sample of size 35 is taken from a normal population, with mean of 65 and standard deviation of 9.3. Describe the sampling distribution of the sample mean.

If a random sample of size n is drawn from a normal population, then the sampling distribution of the sample mean $\bar { X }$ will be:

Which of the following are involved in statistical inference?

Suppose that the time needed to complete a final exam is normally distributed with a mean of 85 minutes and a standard deviation of 18 minutes. a. What is the probability that the total time taken by a group of 100 students will not exceed 8200 minutes? b. What assumption did you have to make in your computations in part (a)?