Study Guide Exam 3 Stats

A 99% confidence interval estimate can be interpreted to mean that a) if all possible samples are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval. b) we have 99% confidence that we have selected a sample whose interval does include the population mean. c) Both of the above. d) None of the above.

Both of the above.

Which of the following is *not true* about the Student's t distribution? a) It has more area in the tails and less in the center than does the normal distribution. b)* It is used to construct confidence intervals for the population mean when the population standard deviation is known.* c) It is bell shaped and symmetrical. d) As the number of degrees of freedom increases, the t distribution approaches the normal distribution.

b) It is used to construct confidence intervals for the population mean when the population standard deviation is known.

The normal distribution is _______________ and symmetric around its mean; that is, one side of the mean is just the mirror image of the other side. The mean, the median, and the mode are all equal for a normally distributed random variable. The normal distribution is completely described by ____ parameters—the population mean μ and the population variance σ2. The population mean describes the central location and the population variance describes the dispersion of the distribution. The normal distribution is ______________ in the sense that the tails get closer and closer to the horizontal axis but never touch it. Thus, theoretically, a normal random variable can assume any value between minus infinity and plus infinity.

bell-shaped two asymptotic

Suppose a 95% confidence interval for turns out to be (1,000, 2,100). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width? a) Increase the sample size. b) Decrease the confidence level. c) Both increase the sample size and decrease the confidence level. d) Both increase the confidence level and decrease the sample size.

c) Both increase the sample size and decrease the confidence level.

The Central Limit Theorem is important in statistics because a) for a large n, it says the population is approximately normal. b) for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size. c) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. - d) for any sized sample, it says the sampling distribution of the sample mean is approximately normal.

c) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.

The width of a confidence interval estimate for a proportion will be a) narrower for 99% confidence than for 95% confidence. b) wider for a sample size of 100 than for a sample size of 50. c) narrower for 90% confidence than for 95% confidence. d) narrower when the sample proportion is 0.50 than when the sample proportion is 0.20.

c) narrower for 90% confidence than for 95% confidence.

The t distribution a) assumes the population is normally distributed. b) approaches the normal distribution as the sample size increases. c) has more area in the tails than does the normal distribution. d) All of the above.

d) All of the above.

Which of the following statements about the sampling distribution of the sample mean is *incorrect*? a) The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large b) The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample means. c) The mean of the sampling distribution of the sample mean is equal to. d) *The standard deviation of the sampling distribution of the sample mean is equal to* .

d) The standard deviation of the sampling distribution of the sample mean is equal to.

The standard error of the mean a)is never larger than the standard deviation of the population. b)decreases as the sample size increases. c)measures the variability of the mean from sample to sample. d)All of the above.

d)All of the above.

A noted feature of the __________________ distribution is that it is "memoryless," thus implying a constant failure rate. In the electric bulb example, it implies that the probability that the bulb will burn out on a given day is independent of whether the bulb has already been used for 10, 100, or 1,000 hours.

exponential

A graph depicting the normal probability density function is often referred to as the ___________ ____________

normal curve or bell curve

a special case of the normal distribution with a mean equal to zero and a standard deviation (or variance) equal to one.

standard normal distribution

The importance of the standard normal distribution arises from the fact that any normal random variable can be _________________ into the standard normal random variable to derive the relevant probabilities.

transformed