Exam 2 - Stats
The standard error of the mean A) decreases as the sample size increases. B) is never larger than the standard deviation of the population. C) measures the variability of the mean from sample to sample. D) All of the above.
decreases as the sample size increases.
If a test of hypothesis has a Type I error probability ( α ) of 0.01, it means that a. if the null hypothesis is true, you reject it 1% of the time. b. if the null hypothesis is false, you don't reject it 1% of the time. c. if the null hypothesis is true, you don't reject it 1% of the time. d. if the null hypothesis is false, you reject it 1% of the time.
if the null hypothesis is true, you reject it 1% of the time.
If, as a result of a hypothesis test, you reject the null hypothesis when it is false, then you have committed a. an acceptance errors. b. a Type II error. c. a Type I error. d. no error.
no error
The standard deviation of a point estimator is called the a. standard deviation b. standard error c. variance of estimation d. point estimator
standard error
Sampling distributions describe the distribution of A) parameters. B) neither parameters nor statistics. C) statistics. D) both parameters and statistics.
statistics
When "S" is used to estimate "σ", the margin of error is computed by using a. t distribution b. the mean of the population c. the mean of the sample d. normal distribution
t distribution
If the expected value of a sample statistic is equal to the parameter it is estimating, then we call that sample statistic A) biased. B) random. C) minimum variance. D) unbiased.
unbiased
A Type I error is committed when a.you don't reject a null hypothesis that is false. b.you don't reject a null hypothesis that is true. c.you reject a null hypothesis that is true. d.you reject a null hypothesis that is false.
you reject a null hypothesis that is true.
The sample statistic "s" is the point estimator of a. σ b. x bar c. μ d. p^
σ
The sample mean is a point estimate of the population mean. True False
True
The sample mean is an unbiased estimator for the population mean. True False
True
The sampling method is independent when the individuals selected for one sample do not dictate which individuals are to be in a second sample. a. True b. False
True
The smaller the p-value, the stronger is the evidence against the null hypothesis. True False
True
The statement of the null hypothesis always contains an equality. True False
True
The t distribution approaches the standardized normal distribution when the number of degrees of freedom increases. True False
True
The t distribution is more dispersed than the normal. a. True b. False
True
The t distribution is used to construct confidence intervals for the population mean when the population standard deviation(𝞂) is unknown. True False
True
The variance of the number of successes in a binomial experiment of n trials is σ 2 = n p (1 - p).
True
To perform inference on the difference of two population means, we must first determine whether the data come from an independent or dependent sample. a. True b. False
True
True or False: A sampling distribution is defined as the probability distribution of all possible sample of same sizes that can be observed from a given population.
True
True or False: If the population distribution is symmetric, the sampling distribution of the sample mean can be approximated by the normal distribution even if the samples contain 15 observations.
True
True or False: The Central Limit Theorem ensures that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.
True
True or False: The sample proportion is an unbiased estimate of the population proportion.
True
The symbol for the confidence coefficient of a statistical test is a. 1 - α. b. 1 - β. c. β. d. α.
1 - α
You know that the probability of committing a Type II error (β) is 5%, you can tell that the power of the test is a.unknown. b. 95%. c. 2.5%. d. 97.5%.
95%
A pharmacist states that a 95% confidence interval for the average price of a particular prescription drug based on a sample of size 100 is $30.50 to $35.50. When asked to explain the meaning of this, the pharmacist says, "the probability that the true average price is between $30.50 and $35.50 is 95%." Is this statement correct? a. True b. False
False
Confidence intervals are useful when trying to estimate unknown statistics True False
False
For a continuous random variable number of outcomes are countable a. True b. False
False
For a given level of significance, increasing the sample size will always decrease the probability of committing a Type I error. a. True b. False
False
For hypothesis tests, the alternative hypothesis always includes the statement of equality between the parameter and the null value. a. True b. False
False
If the calculated value of the test t statistics is negative, then there is strong evidence that the null hypothesis is false. a. True b. False
False
In a hypothesis test, it is irrelevant whether the test is a one-tail or two-tail test. True False
False
The goal of the hypothesis test is to prove the null hypothesis a. True b. False
False
The null hypothesis is the proposition we want to find evidence for in a hypothesis testing. a. True b. False
False
The standard error of the mean increases as the sample size increases. a. True b. False
False
The t-distribution approaches the normal distribution as the number of degrees of freedom decreases. Select one: True False
False
There is no difference between testing a single population mean and testing the difference between two population means. True False
False
True or False: Suppose, in testing a hypothesis about a mean, the p-value is computed to be 0.034. The null hypothesis should be rejected if the chosen level of significance is 0.01.
False
When the population is normal, we can always use a Z-test a. True b. False
False
A hypothesis test is significant when the P-value is greater than β (P(type II error). a. True b. False
Flase
You have created a 95% confidence interval for μ with the result 10 ≤ μ ≤ 15.What decision will you make if you test H0: μ = 16 versus Ha: μ ≠ 16 at α = 0.05? a. Fail to reject H0 in favor of Ha. b. Do not reject H0 in favor of Ha. c. Reject H0 in favor of Ha. d. We cannot tell what our decision will be from the information given.
Reject H0 in favor of Ha.
You compute a 95% confidence interval and a 99% confidence interval for a given data. Which of the following statement is correct? a. The 99% interval is wider b. The 95 % interval is wider c. You cannot be determined which interval is wider unless you know n and s d. The intervals have the same width
The 99% interval is wider
Which of the following would be an appropriate alternative hypothesis? a. The mean of a sample is greater than 55. b. The mean of a sample is equal to 55. c. The mean of a population is greater than 55. d. The mean of a population is equal to 55.
The mean of a population is greater than 55.
A point estimate consists of a single sample statistic that is used to estimate the true population parameter. True False
True
A point estimator is called unbiased if the expected value of the point estimator is equal to the true population parameter. a. True b. False
True
A sampling distribution is a distribution for a statistic. True False
True
As the sample size increases, the t distribution approaches to the standard normal distribution. a. True b. False
True
For a given data set, the confidence interval will be wider for 95% confidence than for 90% confidence. True False
True
For a given sample size, the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced. True False
True
If a test rejects Ho: µ1 = µ2, then the confidence interval for (µ1 - µ2) having the same error probability does not contain zero. a. True b. False
True
If p-value of the test statistic is smaller than α, conclude 'Reject Ho'. a. True b. False
True
If we decrease the confidence coefficient for a fixed n, we decrease the width of the confidence interval. a. True b. False
True
If σ is known, use the z test for μ. The population must be normally distributed if n < 30. a. True b. False
True
If σ is unknown and n < 30, use the t test for testing μ. The population must be approximately normally distributed. a. True b. False
True
Regardless of the degrees of freedom, every t distribution is symmetric around 0. True False
True
Suppose an experiment and a sample size are fixed and a test statistic is chosen. Then, decreasing the size of the rejection region to obtain a smaller α value results in a larger β value for any parameter value consistent with Ha. a. True b. False
True
The appropriate inferential procedure used to "Are ST371 students more likely than ST370 students to be employed full-time" is a hypothesis test for the difference in two proportions. Select one: True False
True
The appropriate inferential procedure used to "Are the majority of registered voters planning to vote in the next presidential election" is a hypothesis test for a single proportion True False
True
The appropriate inferential procedure used to "How much cheese (in pounds) does an average American adult consume annually" is a confidence interval for a single mean. True False
True
The appropriate inferential procedure used to "Is the average age in the population of all ST370 students greater than 30 years" is a hypothesis test for a single mean. True False
True
The appropriate inferential procedure used to "On average, are ST370 students younger than ST371 students" is a hypothesis test for the difference in two means True False
True
The appropriate inferential procedure used to "On average, how much taller are adult male giraffes compared to adult female giraffes" is a confidence interval for the difference in two means. True False
True
The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter. a. True b. False
True
