BUS_228 Unit 3.
True or False: A sampling distribution is defined as the probability distribution of possible sample sizes that can be observed from a given population.
F
True or False: As the sample size increases, the standard error of the mean increases.
F
True or False: As the size of the sample is increased, the standard deviation of the sampling distribution of the sample mean for a normally distributed population will stay the same.
F
A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. The 95% confidence interval for p is 0.59 0.07. Interpret this interval. (a) We are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66. (b) 95% of the students get between 52% and 66% of their tuition paid for by financial aid. (c) We are 95% confident that between 52% and 66% of the sampled students receive some sort of financial aid. (d) We are 95% confident that 59% of the students are on some sort of financial aid.
A
For sample sizes greater than 30, the sampling distribution of the mean will be approximately normally distributed (a) regardless of the shape of the population. (b) only if the shape of the population is symmetrical. (c) only if the standard deviation of the samples are known. (d) only if the population is normally distributed.
A
True or False: The confidence interval obtained will always correctly estimate the population parameter.
F
True or False: The sample mean is a point estimate of the population mean.
T
Sampling distributions describe the distribution of (a) parameters. (b) statistics. (c) both parameters and statistics. (d) neither parameters nor statistics.
B
If the expected value of a sample statistic is equal to the parameter it is estimating, then we call that sample statistic (a) unbiased. (b) minimum variance. (c) biased. (d) random.
A
Which of the following is true about the sampling distribution of the sample mean? (a) The mean of the sampling distribution is always μ. (b) The standard deviation of the sampling distribution is always 𝝈. (c) The shape of the sampling distribution is always approximately normal. (d) All of the above are true.
A
For sample size 16, the sampling distribution of the mean will be approximately normally distributed (a) regardless of the shape of the population. (b) if the shape of the population is symmetrical. (c) if the sample standard deviation is known. (d) if the sample is normally distributed.
B
Suppose a 95% confidence interval for turns out to be (1,000, 2,100). Give a definition of what it means to be "95% confident" in an inference. (a) In repeated sampling, the population parameter would fall in the given interval 95% of the time. (b) In repeated sampling, 95% of the intervals constructed would contain the population mean. (c) 95% of the observations in the entire population fall in the given interval. (d) 95% of the observations in the sample fall in the given interval.
B
The standard error of the mean for a sample of 100 is 30. In order to cut the standard error of the mean to 15, we would (a) increase the sample size to 200. (b) increase the sample size to 400. (c) decrease the sample size to 50. (d) decrease the sample to 25.
B
When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that p is estimated to be, the sample size required __________. (a) is smaller (b) is larger (c) is not affected (d) can be smaller, larger or unaffected
B
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
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.
C
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 sample size 1, the sampling distribution of the mean will be normally distributed (a) regardless of the shape of the population. (b) only if the shape of the population is symmetrical. (c) only if the population values are positive. (d) only if the population is normally distributed.
D
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
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
Which of the following is true regarding the sampling distribution of the mean for a large sample size? (a) It has the same shape, mean, and standard deviation as the population. (b) It has a normal distribution with the same mean and standard deviation as the population. (c) It has the same shape and mean as the population, but has a smaller standard deviation. (d) It has a normal distribution with the same mean as the population but with a smaller standard deviation.
D
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 μ. (d) The standard deviation of the sampling distribution of the sample mean is equal to 𝝈.
D
True or False: If the population distribution is symmetric, the sampling distribution of the mean can be approximated by the normal distribution if the samples contain 15 observations.
F
True or False: The t distribution allows the calculation of confidence intervals for means for small samples when the population variance is not known, regardless of the shape of the distribution in the population.
F
True or False: A point estimate consists of a single sample statistic that is used to estimate the true population parameter.
T
True or False: As the sample size increases, the effect of an extreme value on the sample mean becomes smaller.
T
True or False: If the population distribution is unknown, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.
T
True or False: Other things being equal, as the confidence level for a confidence interval increases, the width of the interval increases.
T
True or False: The Central Limit Theorem ensures that the sampling distribution of the sample mean approaches normal as the sample size increases.
T
True or False: The confidence interval estimate of the population mean is constructed around the sample mean.
T
True or False: The fact that the sample means are less variable than the population data can be observed from the standard error of the mean.
T
True or False: The standard error of the mean is also known as the standard deviation of the sampling distribution of the sample mean.
T
True or False: The standardized normal distribution is used to develop a confidence interval estimate of the population proportion when the sample size is sufficiently large.
T
True or False: The t distribution allows the calculation of confidence intervals for means when the actual standard deviation is not known.
T
True or False: The t distribution approaches the standardized normal distribution when the number of degrees of freedom increases.
T
