Stat 351 True/ False
In order to determine the p-value associated with hypothesis testing about the population mean μ, it is necessary to know the value of the test statistic.
true
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.
false
For statistical inference about the mean of a single population when the population standard deviation is unknown, the degrees for freedom for the t-distribution equal n − 1 because we lose one degree of freedom by using the: a. sample mean as an estimate of the population mean. b. sample standard deviation as an estimate of the population standard deviation. c. sample proportion as an estimate of the population proportion. d. sample size as an estimate of the population size.
a
A Type I error is represented by β.
false
A Type II error is represented by α; it is the probability of rejecting a true null
false
A race car driver tested his car for time from 0 to 60 mph, and in 20 tests obtained an average of 48.5 seconds with a standard deviation of 1.47 seconds. A 95% confidence interval for the 0 to 60 time is 45.2 seconds to 51.8 seconds.
false
If a sample has 15 observations and a 95% confidence estimate for μ is needed, the appropriate value of t is 1.753.
false
In a criminal trial, a Type II error is made when an innocent person is acquitted.
false
In estimating the population mean with the population standard deviation unknown, if the sample size is 16, there are 8 degrees of freedom.
false
In forming a 95% confidence interval for a population mean from a sample size of 20, the number of degrees of freedom from the t-distribution equals 20.
false
In order to interpret the p-value associated with hypothesis testing about the population mean μ, it is necessary to know the value of the test statistic.
false
Increasing the probability of a Type I error will increase the probability of a Type II error.
false
It is possible to commit a Type I error and a Type II error at the same time.
false
Reducing the probability of a Type I error also reduces the probability of a Type II error.
false
The statistic when the sampled population is normal is Student t-distributed with n degrees of freedom.
false
A Type I error is represented by α; it is the probability of rejecting a true null hypothesis.
true
A Type II error is represented by β; it is the probability of failing to reject a false null hypothesis.
true
A null hypothesis is a statement about the value of a population parameter.
true
An alternative or research hypothesis is an assertion that holds if the null hypothesis is false.
true
If a sample has 18 observations and a 90% confidence estimate for μ is needed, the appropriate value of t is 1.740.
true
If the sampled population is nonnormal, the t-test of the population mean μ is still valid, provided that the condition is not extreme.
true
In a criminal trial, a Type I error is made when an innocent person is convicted.
true
In testing a hypothesis, statements for the null and alternative hypotheses as well as the selection of the level of significance should precede the collection and examination of the data.
true
The probability of making a Type I error and the level of significance are the same
true
The statement of the null hypothesis always includes an equals sign (=).
true
The t-distribution assumes that the population is normally distributed.
true
The t-distribution is used in a confidence interval for a mean when the actual standard error is not known.
true
The t-distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown.
true
There is an inverse relationship between the probabilities of Type I and Type II errors; as one increases, the other decreases, and vice versa.
true
