Exam 7: Sampling Methods and the Central Limit Theorem

A new extended-life light bulb has an average service life of 750 hours, with a standard deviation of 50 hours. The shape of this distribution is unknown. From a sample of 100 light bulbs, about what percent of the bulbs will last more than 700 hours?

A retailer claims that 90% of its customers are "pleased" or "very pleased" with the customer service. In a survey of 300 customers taken last week, what is the probability that 84% or more will be "pleased" or "very pleased" with the service?

i. If the sample size keeps getting larger and larger and finally equals the size of the population, there would be no error in predicting the population mean because the sample size and the size of the population would be the same. ii. A simple random sample assumes that each item or person in the population has an equal chance of being included. Iii) We can expect some difference between sample statistics and the corresponding population parameters. This difference is called the sampling error.

70% of North American women have pierced ears. For a survey of 49 women, what is the standard error?

As the sample size (n) increases, does to the spread in the distribution of the sample means increase, decrease, or stay the same?

The mean rent for a two-bedroom apartment in the Greater Toronto Area is $2,000 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 36 two-bedroom apartments and finding the mean to be at least $1,500 per month? The standard deviation of the sample is $300.

Is the mean of a population called a parameter or a statistic?

For a population that is not normally distributed, the distribution of the sample means will:

What is the name of the standard deviation of the sampling distribution of the sample means called ____________.

What sample statistic is used to estimate a population parameter?

Is the standard deviation of the sampling distribution of the mean larger or smaller than the standard deviation of the population under study?

70% of North American women have pierced ears. In a survey of 49 women, what is the probability that less than 30 had pierced ears?

For a sampling distribution of the means, what percent of the means would be between ± 1.96 standard deviations?

It has been estimated that 25% of all university students switch majors within their first two years of starting classes. If a random sample of 500 third-year students is taken at a city university, what is an estimate of the probability that 20% or more had switched majors within their first two years?

The daily sales of a small retail store in Toronto for the last 365 days are normally distributed with a mean of $2,050, and a standard deviation of $300. From a sample of 49 days, what is the probability of having a sample mean more than $2,000?

The mean of all possible sample means is equal to the

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spend studying per week. Based on a simple random sample, they surveyed 144 students. The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours. What is the standard error of the mean?

Which of the following is the standard error of the mean?