Concepts
When the hypothesized difference of the population proportions is equal to 0, we?
1) Are able to estimate the standard error of P1-P2 using the pooled PBar 2) Can use the confidence interval to implement the test if the difference of the population proportions is equal to 0
The choice of an appropriate test for comparing two population means depends on whether we deal with?
1) Qualitative or quantitative date 2) Independent or matched-pairs sampling 3) The equality or lack of equality of population variances
Objective of a hypothesis test?
1) Rejecting the null hypothesis when it is false. 2) Not rejecting the null hypothesis when it is true.
In the test for comparing two population means when population variances are unknown and unequal, the degrees of freedom using the proper formula is 34.7. How many degrees of freedom should be assumed to find the p-value of the test?
34
A trainer works with track and field athletes. She believes that her clients run faster after going through her program for six weeks. How might she test that claim?
A matched pairs hypothesis test for μD
What type of test for population means should be performed when examining a situation in which employees are first tested, then trained, and finally retested?
A t test under dependent sampling
If the sampling distribution of XBar1 - XBar 2 cannot be assumed normal, we?
Are unable to compute a confidence interval
The chi-square test of a contingency table is valid when the expected cell frequencies are:
At least 5
For the goodness-of-fit test, the chi-square test statistic will:
Be at least 0
Suppose you want to determine if gender and major are independent. Which test should you use?
Chi-square test for independence
Suppose you want to determine if mutual funds quarterly returns have a normal distribution using quantitative summary statistics. The most appropriate test is the:
Chi-square test for independence
The alternative hypothesis typically?
Contest the status quo for which a corrective action may be required
What type of data is required to compare prices of the same textbooks sold by two different vendors?
Dependent random samples with quantitative data
HO: μ = 0 and HA: μ ≠ 0. The value of the test statistic is z = -1.38. If we choose a 5% significance level, then we
Do not reject the null hypothesis and conclude that the population mean is not significantly different from zero.
A type 2 error occurs when we
Do not reject the null hypothesis when it is actually false (false negative)
A goodness-of-fit test analyzes for two qualitative variables whereas a chi-square test of a contingency table is for a single qualitative variable. T/F
False
A type 2 error is made when we reject the null and the null is actually false. T/F
False
For a chi-square goodness-of-fit test, the expected category frequencies are calculated using the sample category proportions. T/F
False
For a chi-square test of a contingency table, each observation may be counted in multiple cells of the contingency table. T/F
False
For a multinomial experiment with k categories, the goodness-of-fit test statistic is assumed to follow a chi-square distribution with k degrees of freedom. T/F
False
If the null hypothesis is rejected by the goodness-of-fit test, the alternative hypothesis specify which of the population proportions differ from their hypothesized value. T/F
False
If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution XBar1 - XBar2, is approximately normal only if the sum of the sample observations is sufficiently large-that is, when n1+n2 ≥ 30. T/F
False
On the basis of sample information, we either "accept the null" or reject the null." T/F
False
The alternative hypothesis typically agrees with the status quo. T/F
False
The confidence interval for the difference μ1-μ2 is based on the same approach used in the case of one sample: Point Estimate ± Standard Error. T/F
False
The critical value approach specifies a range of values, also called the rejection region, such that if the value of the test statistic falls into this range, we do not reject the null hypothesis. T/F
False
The difference between the two samples means XBar1 - XBar2 is an interval estimator of the difference between two population means μ1-μ2. T/F
False
The necessary condition for the matched-pairs sample is that the same individual gets sampled twice. T/F
False
Two random samples are considered independent if the observations in the first sample are different from the observations of the second sample. T/F
False
We always deal with the matched-pairs sampling if two samples have the same number of observations. T/F
False
Packaged candies have three different types of colors, suppose you want to determine if the population proportion of each color is the same. The most appropriate test is the:
Goodness-of-fit test for a multinomial experiment
An appropriate set of hypotheses?
H0: μ = 0 HA: μ ≠ 0
One-tailed test
H0: μ ≤ 10 vs. HA: μ > 10 H0: μ ≥ 400 vs. HA: μ < 400
Two-tailed test
HO: μ = 10 vs. HA: μ ≠ 10
Which of the following null hypotheses is used to test if five population proportions are the same?
Ho: p1=p2=p3=p4=p5=.20
What type of data should be collected when examining a situation in which two candidates running in different elections are being compared in their likelihood of winning their elections?
Independent sampling with qualitative data
When comparing two population means, their hypothesized differences
May assume any value
In general, the null and alternative hypotheses are?
Mutually exclusive
When conducting a hypothesis test for a given sample size, if the probability of a type 1 error decreases, then the
Probability of incorrectly accepting the null increases
Decision rules when using the p-value approach to hypothesis testing?
Reject H0 if p-value < α Do not reject H0 if p-value > α
A type 1 error occurs when we
Reject the null hypothesis when it is actually true (false positive)
Which of the following types of test may be performed?
Right-tailed, left-tailed, and two-tailed test
The null hypothesis in a hypothesis test refer to?
The default state of nature.
Which of the following is not a restriction for comparing two population means?
The equality of the sample sizes
If the Null hypothesis is rejected at a 1% significance level, then
The null hypothesis will be rejected at a 5% significance level
Two or more random samples are considered independent if?
The process that generates one sample is completely separate from the process that generate the other sample
For the chi-square test of a contingency table, the expected cell frequencies are found as:
The row total multiplied by the column total divided by the sample size
For a multinomial experiment, which of the following is not true?
The trials are dependent
If the chosen significance level is α = .05, then
There is a 5% probability of rejecting a true null hypothesis
A hypothesis test regarding the population mean (mu) is based on the sampling distribution of the sample mean (X bar). T/F
True
A type 1 error is committed when we reject the null hypothesis which is actually true. T/F
True
As a general guideline, we use the alternative hypothesis as a vehicle to establish something new, or contest the status quo, for which a corrective action may be required. T/F
True
For a chi-square test of a contingency table, the degrees of freedom are calculated as (r - 1)(c - 1) where r and c are the number of rows and columns in the contingency table. T/F
True
For a chi-square test of a contingency table, the expected frequencies for each cell are calculated assuming the null hypothesis is true. T/F
True
For a given sample size, any attempt to reduce the likelihood of making one type of error (1 or 2) will increase the likelihood of the other error. T/F
True
For a statistical inference regarding μ1-μ2, it is imperative that the sampling distribution of XBar1 - XBar2 is normally distributed. T/F
True
In a one-tailed test, the rejection region is located under one tail (left or right) of the corresponding probability distribution, while a two-tailed test this region is located under both tails. T/F
True
In the case when σ^2(1) and σ^2(2) are unknown and can be assumed equal, we can calculate a pooled estimate of the population variance. T/F
True
The chi-square test statistic measures the difference between the observed frequencies and the expected frequencies assuming the null hypothesis is true. T/F
True
The confidence interval for the difference μ1-μ2 equals the standard error SE (XBar1 - XBar2) multiplied by either Z (α/2) or t (α/2,df), depending on whether or not the population variances are known. T/F
True
The null hypothesis typically corresponds to a presumed default state of nature. T/F
True
Under the assumption that the null hypothesis is true as an equality, the p-value is the likelihood of observing a sample mean that is at least as extreme as the on derived from the given sample. T/F
True
We covert the estimate XBar1 - XBar2 into the corresponding value of the z or t test statistic by dividing the difference between XBar1 - XBar2 and the hypothesized difference d0 by the standard error of the estimator XBar1 - XBar2. T/F
True
The chi-square test of a contingency table is a test of independence for:
Two qualitative variables
When calculating the standard error of XBar1 - XBar 2, under what assumption do you pool the sample variances of s^2(1) and s^2(2)
Unknown population variances that are assumed equal
For the goodness-of-fit test, the expected category frequencies found are the:
hypothesized proportions
For the goodness-of-fit test, the sum of the expected frequencies must equal:
n
If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution XBar1 - XBar2, is approximately normal only if the sum of the sample observations is sufficiently large-that is, when n1+n2 ≥ 30.
n1 ≥30, n2 ≥ 30