Quantitative Methods
What type of error occurs if you fail to reject H0 when, in fact, it is not true?
Type II
The sampling distribution used when making inferences about a single population's variance is
a chi-square distribution.
In hypothesis testing, the critical value is
a number that establishes the boundary of the rejection region.
A Type II error is committed when
a true alternative hypothesis is mistakenly rejected.
Which of the following has a chi-square distribution?
((n-1)s^2)/sigma
In a two-tailed hypothesis test, the area in each tail corresponding to the critical values is equal to
α/2.
The sample mean is the point estimator of
μ
The sample statistic s is the point estimator of
σ
It is impossible to construct a frame for a(n) _____ population.
infinite
The value of F.05 with 8 numerator and 19 denominator degrees of freedom is
2.48
The p-value is
a probability.
As the test statistic becomes larger, the p-value
gets smaller.
Doubling the size of the sample will
reduce the standard error of the mean to approximately 70% of its current value.
When s is used to estimate σ, the margin of error is computed by using the
t distribution.
A finite population correction factor is needed in computing the standard deviation of the sampling distribution of sample means
whenever the sample size is more than 5% of the population size.
For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test,
will result in the area corresponding to the critical value being smaller.
The probability of making a Type I error is denoted by
α
The symbol used for the variance of the population is
σ^2
When the following hypotheses are being tested at a level of significance of α H0: μ ≥500 Ha: μ < 500 the null hypothesis will be rejected, if the p-value is
≤α.
In order to test the following hypotheses at an α level of significance H0: μ≤ 800 Ha: μ > 800 the null hypothesis will be rejected, if the test statistic z is
≥ zα
A simple random sample from an infinite population is a sample selected such that
each element is selected independently and from the same population.
The probability distribution of all possible values of the sample mean x ¯ is
the sampling distribution of x ¯x ¯.
The closer the sample mean is to the population mean,
the smaller the sampling error.
In general, higher confidence levels provide
wider confidence intervals.
If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the
width of the confidence interval to increase.
For a lower tail test, the test statistic z is determined to be zero. The p-value for this test is
+0.5
If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient will be
.95
The mean of the t distribution is
0
A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 50 and 5, respectively. The standard error of the mean is
0.5
Consider the following sample information from Population A and Population B. Sample A Sample B n 24 16 s2 32 38 We want to test the hypothesis that the population variances are equal. The test statistic for this problem equals
1.19
A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Today Five Years Ago x ¯ 82 88 σ2 112.5 54 n 45 36 The standard error of x ¯ 1-x ¯ 2 is
2
Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1000) 45 41 Population Variance () 128 72 The standard error of the difference between the two sample means is
2.0
Consider the following sample information from Population A and Population B. Sample A Sample B n 24 16 s2 32 38 We want to test the hypothesis that the population variances are equal. The null hypothesis is to be tested at the 10% level of significance. The critical value from the F distribution table is
2.13
The critical value of F using α = .05 when there is a sample size of 21 for the sample with the smaller variance, and there is a sample size of 9 for the sample with the larger sample variance is
2.45
The following data was collected from a simple random sample of a population. 13 17 18 21 23 The point estimate of the population standard deviation is
3.441
The value of F.01 with 9 numerator and 20 denominator degrees of freedom is
3.46
Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1000) 45 41 Population Variance () 128 72 The point estimate of the difference between the means of the two populations is
4
A sample of 61 observations yielded a sample standard deviation of 6. If we want to test H0: σ2 = 40, the test statistic is
54
In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 58 items is selected. The mean of the sample is determined to be 36. The associated number of degrees of freedom for reading the t value is
57
χ .975 2 = 8.231 indicates that
97.5% of the chi-square values are greater than 8.231.
he sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the
F distribution.
The average manufacturing work week in metropolitan Chattanooga was 40.2 hours last year. It is believed that the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are
H 0: μ ≥ 40.2 H a: μ < 40.2
The average hourly wage of computer programmers with 2 years of experience has been $21.80. Because of high demand for computer programmers, it is believed there has been a significant increase in the average hourly wage of computer programmers. To test whether or not there has been an increase, the correct hypotheses to be tested are
H0: μ ≤ 21.80 Ha: μ > 21.80.
A random sample of 25 employees of a local company has been taken. A 95% confidence interval estimate for the mean systolic blood pressure for all employees of the company is 123 to 139. Which of the following statements is valid?
If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.
Which of the following rejection rules is proper?
Reject H 0 if F ≥ F α.
From a population that is not normally distributed and whose standard deviation is not known, a sample of 50 items is selected to develop an interval estimate for µ. Which of the following statements is true?
The t distribution with 49 degrees of freedom must be used.
As a general guideline, the research hypothesis should be stated as the
alternative hypothesis.
If the null hypothesis is rejected at the .05 level of significance, it will _____ be rejected at the .10 level of significance.
always
For a population with any distribution, the form of the sampling distribution of the sample mean is
always normal for large sample sizes.
Whenever the population has a normal probability distribution, the sampling distribution of x ¯ is a normal probability distribution for
any sample size.
The random variable for a chi-square distribution may assume
any value greater than zero.
A sample of 25 observations is taken from an infinite population. The sampling distribution of p ¯ is
approximately normal if np≥≥5 and n(1-P)≥≥5.
A 95% confidence interval for a population mean is determined to be 100 to 120. For the same data, if the confidence coefficient is reduced to .90, the confidence interval for μ
becomes narrower.
In interval estimation, as the sample size becomes larger, the interval estimate
becomes narrower.
As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution
becomes smaller.
When the level of confidence decreases, the margin of error
becomes smaller.
Using an α = .04, a confidence interval for a population proportion is determined to be .65 to .75. For the same data, if α is decreased, the confidence interval for the population proportion
becomes wider.
If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means
can be approximated by a normal distribution.
For the following hypothesis test, H0: μ ≥ 150 Ha: μ < 150 the test statistic
can be either negative or positive.
For an F distribution, the number of degrees of freedom for the numerator
can be larger, smaller, or equal to the number of degrees of freedom for the denominator.
The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size is large is based on the
central limit theorem.
The sampling distribution of the quantity (n - 1)s2/σ2 is the
chi-square distribution.
The ability of an interval estimate to contain the value of the population parameter is described by the
confidence level.
In point estimation
data from the sample is used to estimate the population parameter.
As the sample size increases, the margin of error
decreases.
The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the
degrees of freedom.
The desired situation is when the sampled population is _____ the targeted population.
identical to
The population being studied is usually considered _____ if it involves an ongoing process that makes listing or counting every element in the population impossible.
infinite
An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the
interval estimate.
The level of significance α
is (1 - confidence coefficient).
To compute an interval estimate for the difference between the means of two populations, the t distribution
is not restricted to small sample situations.
For a given confidence level and when σ is known, the margin of error in a confidence interval estimate
is the same for all samples of the same size.
When the area corresponding to the critical value is in the lower tail of the sampling distribution, the p-value is the area under the curve
less than or equal to the test statistic.
The value added to and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the
margin of error.
When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as _____ samples.
matched
The level of significance is the
maximum allowable probability of Type I error.
If the null hypothesis is rejected at the 5% level of significance, it _____ at the 1% level.
may be rejected or not rejected
The p-value
must be a number between zero and one.
A two-tailed test is performed at the .05 level of significance. The p-value is determined to be .01. The null hypothesis
must be rejected.
A sample of n observations is taken from a normal population. The appropriate chi-square distribution has
n - 1 degrees of freedom.
When developing an interval estimate for the difference between two population means with sample sizes of n 1 and n 2.
n 1and n 2 can be of different sizes.
When constructing a confidence interval for the population mean using the standard deviation of the sample, the degrees of freedom for the t distribution equals
n-1
In computing the standard error of the mean, the finite population correction factor is used when
n/N > 0.05.
As the degrees of freedom increase, the t distribution approaches the _____ distribution.
normal
A sample of 200 elements from a population with a known standard deviation is selected. For an interval estimation of μ, the proper distribution to use is the
normal distribution.
For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is the
normal distribution.
A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of x ¯ is
normal if the population is normally distributed.
As a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever
np ≥5 and n(1-p) ≥5.
Two approaches to drawing a conclusion in a hypothesis test are
p-value and critical value.
When the p-value is used for hypothesis testing, the null hypothesis is rejected if
p-value ≤ α.
When the p-value is used for hypothesis testing, the null hypothesis is rejected if
p-value ≤α.
The general form of an interval estimate of a population mean or a population proportion is the _____ plus and minus the _____.
point estimate, margin of error
A single numerical value used as an estimate of a population parameter is known as a
point estimate.
The sample statistic, such as x ¯, s, or p ¯, that provides the point estimate of the population parameter is known as a
point estimator.
The purpose of statistical inference is to provide information about the
population based upon information contained in the sample.
Which of the following is(are) point estimator(s)?
s
The symbol used for the variance of the sample is
s^2
Which of the following has an F distribution?
s^2 1/s^2 2
The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the
same as α.
The margin of error in an interval estimate of the population mean is a function of all of the following except
sample mean.
The degrees of freedom associated with a t distribution are a function of the
sample size.
In interval estimation, the t distribution is applicable only when the
sample standard deviation is used to estimate the population standard deviation.
The t distribution should be used whenever the
sample standard deviation is used to estimate the population standard deviation.
The value of the _____ is used to estimate the value of the population parameter
sample statistic
To avoid the problem of not having access to tables of the F distribution when a one-tailed test is required and with F values given for the lower tail, let the
sample variance from the population with the smaller hypothesized variance be the numerator of the test statistic.
Consider the following sample information from Population A and Population B. Sample A Sample B n 24 16 s2 32 38 We want to test the hypothesis that the population variances are equal. At the 10% level of significance, the null hypothesis
should not be rejected.
For a lower tail test, the p-value is the probability of obtaining a value for the test statistic at least as
small as that provided by the sample.
More evidence against H0 is indicated by
smaller p-values.
The standard error of two sample means is the
standard deviation of the sampling distribution of sample mean.
The standard error of x ¯ 1 − x ¯ 2 is the
standard deviation of the sampling distribution of x ¯ 1 − x ¯ 2.
The standard deviation of p ¯ is referred to as the _____ proportion.
standard error of the
As the sample size increases, the
standard error of the mean decreases.
The standard deviation of a point estimator is called the
standard error.
The population we want to make inferences about is the
target population.
If the null hypothesis is rejected in hypothesis testing,
the alternative hypothesis is true.
To avoid the problem of not having access to Tables of F distribution when F values are needed for the lower tail, the numerator of the test statistic for a two-tailed test should be the one with
the larger sample variance.
The probability of committing a Type I error when the null hypothesis is true as an equality is
the level of significance
The p-value is a probability that measures the support (or lack of support) for
the null hypothesis.
A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have _____ of being selected.
the same probability
