CISB 241 Test 2 Chapters 8-14
In analyzing the relationship between two numeric variables, a scatter plot can be used to detect which of the following?
- A positive linear relationship - A curvilinear relationship - A negative linear relationship
A confidence interval on the mean:
- Calculates a range of possible values for the population mean. - Is needed when the population mean is unknown and it is difficult to collect all possible values in the population. - Uses a sample from the population to estimate the population mean.
In a one-way ANOVA, which of the following is true?
- The degrees of freedom associated with the between sum of squares is equal to one less than the number of populations. - The critical value will be an F-value from the F distribution. - If the null hypothesis is rejected, it may still be possible that two or more of the population means are equal.
If a hypothesis test for a single population variance is to be conducted, which of the following statements is true?
- The null hypothesis must be stated in terms of the population variance. - The chi-square distribution is used. - If the sample size is increased, the critical value is also increased for a given level of statistical significance.
Which of the following statements is true with respect to the t-distribution?
- The t-distribution is symmetrical. - The exact shape of the t-distribution depends on the number of degrees of freedom. - The t-distribution is more spread out than the standard normal distribution.
Given the result of a contingency analysis is to reject Ho and the two categories are found to be dependent:
- This means the chi-square was larger enough to be in the upper tail. - To find a potential pattern, you could review the cells where there is the largest difference between the observed and expected values that also have high chi-square values. - Further study and testing will be needed to conducted to prove what the relationships might be.
Under what conditions can the t-distribution be correctly employed to test the difference between two population means?
- When the population variances are unknown - When the two populations of interest are assumed to be normally distributed - When the population variances are assumed to be equal
When the the observed value of one or more cells is less than 5, which of the following is true?
- You could increase the overall sample size. - You could try to combine categories when some categories have some natural fit together. - If Ho is not rejected (there was not enough difference between the expected and observed values), then there is no issue with a Type I error and no need for further action.
A cell phone company wants to determine if the use of text messaging is independent of age. The following data has been collected from a random sample of customers. Regularly use text messaging Do not regularly use text messaging Under 21 82 38 21-39 57 34 40 and over 6 83 To conduct a contingency analysis, the number of degrees of freedom is:
2
The first phase of a hypothesis test is to determine what we are testing. Which of the following is not mentioned as a type of hypothesis test?
A similarity test that proves a value is equal to a desired value.
In conducting a one-way analysis of variance where the critical value = 41.2 and the test statistic = 31.6, which of the following is correct?
Conclude that all means are the same and there is no need to conduct the Tukey-Kramer procedure
Which distribution is used in testing the hypotheses about the equality of two population variances?
F - Distribution
A conclusion to "not reject" the null hypothesis is the same as the decision to "accept" the null hypothesis.
False
A correlation coefficient (r) of -0.9 indicates a weak linear relationship between the variables
False
A joint frequency distribution and contingency analysis can only be completed when the original data is quantitative (numeric data).
False
A large tire manufacturing company has claimed that its top line tire will average more than 80,000 miles. If a consumer group wished to test this claim, they would formulate the following null and alternative hypotheses: Ho: μ ≥ 80,000 Ha: μ ≠ 80,000
False
A sample of n observations is taken from a normally distributed population to estimate the population variance. The degrees of freedom for the chi-square distribution are n-2.
False
Decreasing the level of confidence increases the width of confidence interval.
False
If a hypothesis test is conducted for a population mean, a null and alternative hypothesis of the form: Ho: μ = 100 Ha: µ ≠ 100 will result in a one-tailed hypothesis test since the sample result can fall in only one tail
False
If two variables are highly correlated, it not only means that they are linearly related, it also means that a change in one variable will cause a change in the other variable.
False
In a one-way analysis of variance test, the following null and alternative hypotheses are appropriate: Ho: μ1 = μ2 = μ3 Ha: μ1 ≠ μ2 ≠ μ3
False
In conducting a test of independence for a contingency table that has 4 rows and 3 columns, the number of degrees of freedom is 11.
False
In conducting one-way analysis of variance, the sample size for each group must be equal.
False
In developing a scatter plot, it is proper to draw lines between all the points.
False
It is appropriate to use a t-score using the pilot sample size instead of z in following equation to find the needed sample size? n = (z*stdeve)^2
False
One of the major automobile makers has developed two new engines. At question is whether the two engines have the same variability with respect to miles per gallon. The appropriate null and alternative hypothesis are: Ho: σ12 ≠ σ22 Ha: σ12 = σ22
False
The managers for a vegetable canning facility claim the standard deviation for the ounces per can on the new automated line is less than for the older manual line. Given this, the correct null and alternative hypotheses for performing the statistical test are: Ho: σ1 = σ2 Ha: σ1 ≠ σ2
False
The police chief in a local city claims that the average speed for cars and trucks on a stretch of road near a school is at least 45 mph. If this claim is to be tested, the null and alternative hypotheses are: Ho: µ < 45 Ha: µ ≥ 45
False
The t-distribution is used to test whether two sample variances are equal.
False
The test statistic that is used when testing a null hypothesis for a population variance is the standard normal z-value
False
When determining sample size for a proportion, using p = 0.5 will produce the smallest possible value for n
False
In a contingency analysis, the greater the difference between the actual and the expected frequencies, the larger the chi-square value and the more likely:
H0 should be rejected.
There have been complaints recently from homeowners in the north end claiming that their homes have been assessed at values that are too high compared with other parts of town. They say that the mean increase from last year to this year has been higher in their part of town than elsewhere. To test this, the assessor's office staff plans to select a random sample of north end properties (group 1) and a random sample of properties from other areas within the city (group 2) and perform a hypothesis test. Based on the information provided, the research (or alternate) hypothesis is:
Ha: µ1 > µ2
It is believed the SAT scores for students entering two universities may have different standard deviations. Specifically, it is believed the standard deviation at University A is greater than the standard deviation at University B. If a statistical test is to be conducted, which of the following would be the proper way to formulate the alternative hypothesis?
Ha: σA2 > σB2
A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces. The standard deviation is known to be 0.20 ounces. Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles, which of the following would be the correct formulation of the null and alternative hypotheses?
Ho: µ = 16 Ha: µ ≠ 16
If an economist wishes to determine whether there is evidence that average family income in a community exceeds $25,000. The best null and alternative hypothesis is:
Ho: µ ≤ 25,000 Ha: µ > 25,000
A commuter has two different routes available to drive to work. She wants to test whether route A is faster than route B. The best hypotheses are:
Ho: µA - µB ≥ 0 Ha: µA - µB < 0
A recent study posed the question about whether Japanese are managers more motivated than American managers. A randomly selected sample of each was administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. American Japanese Sample Size 211 100 Mean SSATL Score 65.75 79.83 Population Std. Dev. 11.07 6.41 Which of the following is the correct the null and alternative hypotheses to determine if the average SSATL score of Japanese managers differs from the average SSATL score of American managers?
Ho: µA = µJ Ha: µA ≠ µJ
An analyst plans to test whether the standard deviation for the time it takes bank tellers to provide service to customers exceeds the standard of 1.5 minutes. The correct null and alternative hypothesis for this test are:
Ho: σ2 ≤ 2.25 Ha: σ2 > 2.25
Which of the following is the appropriate null hypothesis when testing whether two population variances are equal?
Ho: σ21 = σ22
A potato chip manufacturer has found that in the past the standard deviation of bag weight has been 0.2 ounces. They want to test whether the standard deviation has changed. The null hypothesis is:
Ho: σ^2 = 0.04
A hotel chain has four hotels in Oregon. The general manager is interested in determining whether the mean length of stay is the same or different for the four hotels. She selects a random sample of n = 20 guests at each hotel and determines the number of nights they stayed. Assuming that she plans to test this using an alpha level equal to 0.05, which of the following is the appropriate alternative hypothesis?
Not all population means are equal.
To use contingency analysis for numerical data, which of the following is true?
Numerical data should be grouped into numeric ranges to get them into categories.
The cost of a college education has increased at a much faster rate than costs in general over the past twenty years. In order to compensate for this, many students work part- or full-time in addition to attending classes. At one university, it is believed that the average hours students work per week exceeds 20. To test this at a significance level of 0.05, a random sample of n = 20 students was selected and their weekly work hours recorded. Given we are trying to prove the hours are more than 20, this goes into Ha as follows: Ho: μ ≤ 20 hours Ha: μ > 20 hours Which of the following is a correct rejection statement?
Reject Ho if t > 1.729
Assume you are conducting a one-way analysis of variance using a 0.05 level of significance and have found that the p-value = 0.02. Which of the follow is correct regarding what you can conclude?
Reject the null hypothesis; at least two of the means are different.
For a chi-square test involving a contingency table, suppose H0 is rejected. We conclude that the two variables are:
Related
Graphing a 90% confidence interval on a normal curve:
The 90% is centered with 5% in each tail.
When testing a two-tailed hypothesis using a significance level of 0.05, a sample size of n = 16, and s=5.2, which of the following is true?
The alpha probability must be split in half with 2.5% in the lower tail and 2.5% in the upper tail.
How can the degrees of freedom be found in a contingency table with cross-classified data?
The df are equal to (number of rows minus 1) multiplied by (number of columns minus 1)
Which of the following applies to a point estimate?
The point estimate is subject to sampling error and will almost always be different from the population value.
When testing/estimating the difference between two means using the method where sample variances are pooled, which of the following assumptions is not needed?
The sample sizes are equal.
In order for a one-way analysis of variance to be considered a balanced design, which of the following must hold?
The sample sizes selected from each population must be equal.
If the population correlation between two variables is determined to be -0.70, which of the following is known to be true?
There is a fairly strong negative linear relationship between the two variables.
A 95% confidence interval on the mean tells us that 95% of all possible samples will have the population mean within the calculated range.
True
A correlation coefficient (r) is computed from a sample and is subject to sampling error. The hypothesis test to see if there the correlation coeffiecent is 0 (meaning no correlation) would use the greek r which is represented as ρ (rho) when writing Ho and Ha.
True
A critical value for a hypothesis test on a mean could be the z or t value that is associated with the acceptable percent of error (alpha) in the tail(s) of the curve. These can be found using either =norm.s.inv(%) or t.inv(%,n-1).
True
A recent study of students at the university contained data on year in school and student age. An appropriate tool for analyzing the relationship between these two variables would be a joint frequency distribution followed by a contingency analysis.
True
A two-tailed hypothesis test with alpha = 0.05 is similar to a 95 percent confidence interval.
True
A two-tailed test for two population variances could have a null hypothesis like the following: Ho: σ21 = σ22
True
An expected cell value of 5 or more is important to ensure an error is not made in the decision making process.
True
Box-and-whisker plots are often useful for determining whether one or more populations might be normally distributed.
True
Contingency analysis helps to make decisions when multiple proportions are involved.
True
For a given significance level, increasing the sample size will tend to increase the chi-square critical value used in testing the null hypothesis about a population variance.
True
Hypothesis testing is about proving something beyond a reasonable doubt
True
In Excel a joint frequency distribution table can be created using a tool called PivotTable.
True
In a contingency analysis the expected values are based on the assumption that the two variables are independent of each other.
True
In conducing one-way analysis of variance, the population distributions are assumed normally distributed.
True
In determining the required sample size when estimating a population proportion, it is necessary to start with some idea of what that proportion is.
True
In estimating a population proportion, the factors that are needed to determine the required sample size are the confidence level, the margin of error and some idea of what the population proportion is
True
Managers use contingency analysis to determine whether two categorical variables are independent of each other.
True
Of the two types of statistical errors, the one that decision makers have most control over is Type I error (the value of alpha).
True
Recently, a company tested three different machine types to see if there was a difference in the mean thickness of products produced by the three. A random sample of ten products was selected from the output from each machine. Given this information, the proper design to test whether the means are equal is a one-way ANOVA balanced design.
True
The F-distribution can only have positive values.
True
The coefficient of determination (R Square) is always found by taking the correlation coefficient (r) and squaring it.
True
The one-way ANOVA test involves assuming that the population variances are equal.
True
The point estimate when calculating a confidence interval on the population average is the sample mean
True
The pooled variance mathematically combines the variances of the two populations and combines it into a single value.
True
The proportions in the joint frequency table can be used to find relative probability for a specified category.
True
The test statistic for the mean is the value calculated from the sample using =(xbar-µ)/(stdev/sqrt(n).
True
To employ contingency analysis, we set up a 2-dimensional table with rows and columns called a contingency table, which can also be referred to as a cross-tabulation or a joint frequency table.
True
Two samples are independent when the occurrence of values in one sample has no influence on the probability of the occurrence of values in the second sample.
True
When calculating a confidence interval, the reason for using the t-distribution rather than the normal distribution for the critical value is that the population standard deviation is unknown.
True
When calculating n-size based on a desired margin of error and confidence level, if you find that n=45.2, you should round up to n=46 to make sure you have a sample size large enough.
True
When constructing a scatter plot, the dependent variable (what we are trying to predict) is placed on the vertical y-axis and the independent variable is placed on the horizontal x-axis.
True
When determining the sample size for a proportion, if you have no previous information available to estimate p, then the best value to use is p = 0.5.
True
When the slope in the regression equation is negative, the correlation coefficient (r) will always be negative.
True
When using a chi-square test for the variance of one population, we are assuming that the population is normally distributed.
True
When writing the null and alternative hypothesis, which of the following is not true:
When testing for a mean, Ho and Ha is testing xbar. Example, Ho: xbar = 12.
Order the steps of a hypothesis test (1-5):
__4__ Statistical Conclusion: Reject Ho, based on the sample there is enough evidence to show <insert text from Ha> or Do not reject Ho, based on the sample there is not enough evidence to show <insert text from Ha> __5__ Business Conclusion: What does this mean in relation to the business? How could you use the information? __2__ How are we measuring it? What is the critical value for the test? Reject Ho if ________ i.e., z-value or t-value (from the charts) or p-value __3__ Calculate the value from the sample i.e., use the sample information to calulate the sample z or t or p __1__ What are we trying to test/show? Formulate the null and alternative hypothesis: Ho: Ha:
When a hypothesis test is to be conducted regarding a population variance, the test statistic will be:
a Χ^2 value from the chi-square distribution.
Given the following information, calculate the degrees of freedom(df) that should be used in the pooled-standard deviation t-test. s12= 4 s22 = 6 n1 = 16 n2 = 25
df = 39
The general format for a confidence interval is:
point estimate +- (critical value)(standard error).
When using the Tukey Kramer procedure, you will need to find the q-value using Appendix I in your textbook
q = 4.05
Your company wants to compare 3 similar products. One aspect is to test how long the product will last. Product research records 10 samples from each of the three products. A one-way ANOVA test concludes at least one mean is different. What is the q-value that is needed for the Tukey-Kramer test using α = .01
q = 4.55
A recent study posed the question about whether Japanese managers are more motivated than American managers. A randomly selected independent sampling method was administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. American Japanese Sample Size 211 100 Mean SSATL Score 65.75 79.83 Sample Std. Dev. 11.07 6.41 A test on the variances was done first and concluded the the standard deviation between the two samples are not equal. Looking at the formula sheet, which test would be most appropriate?
t-test, assuming unequal variances, where d.f. =complex formula
A hypothesis test for the difference between two means is considered a two-tailed test when:
the null hypothesis states that the population means are equal.
Joint frequency distributions are used to display:
the number of occurrences at each of the possible joint occurrences of two variables.
The reason for using the t-distribution in a hypothesis test about the population mean is:
the population standard deviation is unknown.
The purpose of a pilot sample is:
to provide an idea of what the population standard deviation might be.
If a hypothesis test for a single population variance is to be conducted using a significance level of to 0.10, a sample size of n = 16, and the test is a one-tailed upper-tail test, the critical value is:
Χ^2 = 22.3071.
