BSTAT
A simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.
True
For any sample size n, the sampling distribution of X is normal if the population from which the sample is drawn is normally distributed.
True
If a random sample of size n is taken from a normal population with a finite variance, then the statistic T=X-u/SIVn follows the tdf distribution with (n − 1) degrees of freedom, df.
True
In a one-tailed test, the rejection region is located under one tail (left or right) of the corresponding probability distribution, while in a two-tailed test this region is located under both tails.
True
Non -response bias occurs when those responding to a survey or poll are systematically different from the non-respondents.
True
Selection bias occurs when the sample is mistakenly not selected from the target population.
True
The main ingredient for developing a confidence interval is the sampling distribution of the underlying statistic.
True
The margin of error in the confidence interval for the difference equals the standard error multiplied by either or depending on whether or not the population variances are known.
True
The statistical inference concerning the difference between two population proportions is used for qualitative data.
True
A sample regression equation is given by = −100 + 0.5x. If x = 20, the value of y is ________.
Unknown
When calculating the standard error of X1-X2, under what assumption do you pool the sample variances s21 and s21 ?
Unknown population variances that are assumed equal.
Which of the following is true about statistics such as the sample mean or sample proportion?
A statistic is a random variable.
Which of the following is true about statistics such as the sample mean or sample proportion?
A statistic is not a parameter.
A 99% confidence interval estimate can be interpreted to mean that
if all possible samples of the same size are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval.
The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The p-value for this hypothesis test would be ______.
0.0957
If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution of X1-X2 is approximately normal only if the sum of the sample observations is sufficiently large—that is, when n1+n2≥ 30
False If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution of X1-X2 is approximately normal only if both sample sizes are sufficiently large—that is, when n1≥30 and n2≥30
In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour of shopping. Based on previous years, the population standard deviation is thought to be $21 per hour of shopping. Assuming that the amount spent per hour of shopping is normally distributed, find a 90% confidence interval for the mean amount.
[$45.36, $62.64]
Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, 144 supported A. Construct a 99% confidence interval on the population proportion for the support of candidate A in the following election.
[0.4057, 0.5543]
Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, 98 supported candidate B and 58 supported candidate C. Construct a 99% confidence interval on the population proportion for the support of candidate A in the following election.
[0.4057, 0.5543]
We draw a random sample of size 25 from the normal population with variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean?
[11.7019, 13.2981]
For any sample size n, the sampling distribution of is normal even if the population from which the sample is drawn has any distribution.
False
A residual is the difference between the predicted and observed values of y.
False A residual is the differenced between the observed and predicted values of y.
The value 0.75 of a sample correlation coefficient indicates a stronger linear relationship than that of -0.90.
False As the absolute value of the sample correlation coefficient increases, the linear relationship between x and y becomes stronger.
For a given confidence level 100(1-a)% and sample size n, the width of the confidence interval for the population mean is narrower, the greater the population standard deviation σ.
False For a given confidence level and sample size n, the width of the confidence interval for the population mean is wider, the greater the population standard deviation σ.
For a given sample size n and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the confidence level 100(1-a)%
False For a given sample size n and population standard deviation σ, the width of the interval is wider, the greater the confidence level 100(1-a)%
The following scatterplot indicates that the relationship between the two variables x and y is ________.
strong and negative
The following scatterplot indicates that the relationship between the two variables x and y is ________.
strong and positive
Do men really spend more money on St. Patrick's Day as compared to women? A recent survey found that men spend an average of $43.87 while women spend an average of $29.54. Assume that these data were based on a sample of 100 men and 100 women and the population standard deviations of spending for men and women are $32 and $25, respectively. Which of the following is the correct value of test statistic?
z = 3.53
A random sample of size 100 is taken from a population described by the proportion p = 0.06. What are the expected value and the standard error for the sampling distribution of the sample proportion?
0.060 and 0.024
Which of the following are one-tailed tests?
Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400
Statistics are used to estimate population parameters, particularly when it is impossible or too expensive to poll an entire population. A particular value of a statistic is referred to as a(n) ______.
Estimate
The deterministic component of a linear regression model is due to the omission of relevant factors that influence the response variable.
False The deterministic component of a linear regression model is when the value of the response variable is uniquely determined by the values of the explanatory variables. The stochastic component is due to the omission of relevant variables that influence the response.
Assume the competing hypotheses take the following form: H0: µ1 - µ2 = 0, HA: µ1 - µ2 ≠ 0, where µ1 is the population mean for population 1 and µ2 is the population mean for population 2. Also assume that the populations are normally distributed and that the observations in the two samples are independent. The population variances are not known but are assumed equal. Which of the following expressions is appropriate test statistic?
tdf=(x1-x2)/Vs2p(1/n1+1/n2)
A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type II error would be that____________________________.
the franchiser does not build on an acceptable site
According to the central limit theorem, the distribution of the sample mean is always normal if ______.
the sample size n ≥ 30
The GPA of accounting students in a university is known to be normally distributed. A random sample of 20 accounting students results in a mean of 2.92 and a standard deviation of 0.16. Construct the 95% confidence interval for the mean GPA of all accounting students at this university.
2.93 + 2.093(0.16/V20 plus is w line under/ V= square root
Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. Given a sample of four electricians, what is the standard deviation for the sampling distribution of the sample mean?
6,000
In cluster random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called clusters. A cluster sample includes randomly selected observations from each cluster, which are proportional to the cluster's size.
False In cluster random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called clusters. A cluster sample includes observations from randomly selected clusters. Instead of taking a subset from each cluster, the entire cluster is selected as part of the sample.
Nonresponse bias occurs when those responding to a survey or poll are systematically the same as the non-respondents.
False Nonresponse bias occurs when those responding to a survey or poll differ systematically from the nonrespondents.
Selection bias occurs when the sample is mistakenly divided into strata, and random samples are drawn from each stratum.
False Selection bias refers to a systematic exclusion of certain groups from consideration for the sample.
The covariance and correlation coefficient are measures that quantify the non-linear relationship between two variables.
False The covariance and correlation coefficient are measures that quantify the linear relationship between two variables.
The covariance can be use to determine the strength of a linear relationship between two variables.
False The covariance ranges from−infinity to infinity and is sensitive to the units of measurement. As a result, it is hard to determine what are small and large values, and cannot be easily used to assess the strength of a linear relationship.
The difference between the two sample means X1-X2 is an interval estimator of the difference between two population means u1-u2.
False The difference between the two sample means X1-X2 is a point estimator of the difference between two population means u1-u2.
The sample correlation coefficient cannot equal zero.
False The sample correlation coefficient falls between −1 and 1. If it equals 1 (or −1), then a perfect positive (negative) linear relationship exists. If the sample correlation coefficient is zero, then no linear relationship exists.
The correlation coefficient can only range between 0 and 1.
False The sample correlation coefficient falls between −1 and 1. If it equals 1 (or −1), then a perfect positive (or negative) linear relationship exists. If the sample correlation coefficient is zero, then no linear relationship exists.
A simple random sample is a sample of n observations that has a different probability of being selected from the population as any other sample of n observations.
False Most statistical methods presume simple random sample.
A recent Health of Boston report suggests that a greater percentage of female residents suffer from asthma as opposed to males. Suppose that out of 250 females and 200 males that responded to a recent study, 14% and 6% had asthma respectively. Which of the following is the correct conclusion for the test at if the test statistic is found to be 2.76?
Reject H0: p1 − p2 ≤ 0 and therefore conclude that females suffer more from asthma than males.
Do men really spend more money on St. Patrick's Day as compared to women? A recent survey found that men spend an average of $43.87 while women spend an average of $29.54. Assume that these data were based on a sample of 100 men and 100 women and the population standard deviations of spending for men and women are $32 and $25, respectively. Using 1% confidence level, which of the following is the correct conclusion for this test?
Reject H0: µ1 − µ2 ≤ 0 and therefore conclude that on average men spend more money than women on St. Patrick's Day.
According to the central limit theorem, the distribution of the sample means is normal if ______.
the underlying population is normal