E370 Exam 3
Most common way to construct a confidence interval
Point estimate ± Margin of error
Whenever estimating the confidence interval for the population proportion, which of the following is required?
The sample size and the population proportion should be such that np ≥ 5 and n(1 - p) ≥ 5.
As the confidence level decreases, the confidence interval becomes
narrower
For the confidence interval of the mean when the population standard deviation is known and the sample is large, the proper distribution to use is the t distribution with n - 1 degrees of freedom the binomial distribution the standard normal distribution the t distribution with n degrees of freedom
the standard normal distribution
For the interval estimation of µ when σ is known and the sample is large, the proper distribution to use is
the standard normal distribution
When s is used to estimate σ, the margin of error is computed by using
the t distribution
The confidence intervals for the population proportion are generally based on
the z distribution
An estimate is a value of a sample statistic for a particular sample rather than the value of the population parameter or the statistic itself.
true
In a one-tail test, the rejection region is located under one tail (upper or lower) of the corresponding sampling distribution, while in a two-tail test this region is located under both tails.
true
In the hypothesis tests, the null hypothesis is believed to be true unless there is overwhelming evidence to the contrary.
true
It is known that the population data is not normally distributed. Also, the population standard deviation is not known. A sample of 6 items is selected from this population to develop an interval estimate for the mean of the population (µ).
The sample size must be increased for constructing a reliable confidence interval.
When a statistic is used to estimate a parameter, the statistic is referred to as an estimator. A particular value of the estimator is called an estimate.
True
What type of error occurs if you fail to reject H0 when, in fact, it is not true?
Type II error is made when we do not reject the null hypothesis and the null hypothesis is actually false
Given that a 95% confidence interval for the population mean is (6.5, 12.5), we can state the following:
We expect that 95% of all possible sample means drawn from the population will produce confidence intervals that include the population's mean (which makes us 95% confident that interval (6.5, 12.5) contains the population mean).
The alternative hypothesis typically
contest the status quo
As the sample size n increases, the margin of error
decreases
What assumptions did you make when constructing the confidence interval?
np≥5 and n(1−p)≥5.
Which is the following represents an estimate? x¯ p μ=3 s=3
s=3
Which is the following represents an estimator? s^2 σ2 μ p¯=0.4
s^2
A Type I error is committed when we reject the null hypothesis when the null hypothesis is actually true
true
A point estimator refers to an estimator that provides a single value.
true
On the basis of sample information, we can either "accept the null hypothesis" or "reject the null hypothesis".
False, we either "reject the null hypothesis" or "do not reject the null hypothesis".
Which of the following represents an appropriate set of hypotheses?
H0:μ=0; H1:μ≠0
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. To establish whether the mean GPA exceeds 3.50, the appropriate hypotheses are
H0:μ≤3.50; H1:μ>3.50
Which of the following represents an appropriate NULL hypothesis in the lower tail test?
H0:μ≥0
For a given confidence level and sample size, which of the following is true in the interval estimation of the population mean when σ is known?
If the population standard deviation is larger, the interval is wider.
After computing a confidence interval, a researcher believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation for this researcher?
Increase the sample size
Consider the following hypotheses that relate to the medical field: H0: A person is free of disease H1: A person has disease In this example, when the Type I error is commited, we conclude that Multiple choice question
the person is sick or has a disease.
In order to construct the interval estimate of the population mean µ when σ is known and the sample is very small,
the population data must be normally distributed
We use the standard normal distribution to estimate the confidence interval of the mean when
the population standard deviation is known.
The t distribution with n - 1 degrees of freedom is used when
the sample standard deviation is used in the estimation.
If an interval estimate is said to be constructed at the 95% confidence level, the significance level is
0.05
In the point estimation,
data from the sample is used to estimate the population parameter
The hypothesis statement H0:μ≠5H0:μ≠5 is an example of
the alternative hypothesis in a two-tail test
In order to determine a confidence interval for the mean of a population with an unknown standard deviation, a sample of 191 items is selected. The mean of the sample is determined to be 28. The number of degrees of freedom for the critical t value is
190
A simple random sample of 5 observations from a population containing 200 elements was taken, and the following values were obtained: 26 11 26 12 25 A point estimate of the population mean is:
20
A simple random sample of 81 observations was taken from a large population. The sample mean and the standard deviation were determined to be 405 and 81 respectively. The estimated standard error of the mean is
9
Which of the following types of tests about the population parameter may be performed?
Upper-tail, lower-tail, and two-tail tests
Confidence intervals for the population mean may be created for the cases when the population standard deviation is known or unknown. How are these two cases treated differently?
Use the z distribution when σ is known; use the t distribution when σ is unknown.
As the number of degrees of freedom for the t distribution increases, the difference between the t distribution and the standard normal distribution
becomes smaller
The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the
margin of error
As the sample size n increases, the confidence interval becomes
narrower
The sample standard deviation, s, is the point estimator of the
population standard deviation σ
When conducting a hypothesis test for the population mean when the population standard deviation is known, the critical value and the p-value are computed using
standard normal distribution
When s is used to estimate the confidence interval for the mean, the margin of error is computed by using
t distribution
