A confidence interval on the mean:
#NAME?
The point estimate when calculating a confidence interval on the population average is the sample mean.
TRUE
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.
Which of the following is not true about a confidence interval?
...
Graphing a 90% confidence interval on a normal curve:
The 90% is centered with 5% in each tail.
Decreasing the level of confidence increases the width of confidence interval.
FALSE
The general format for a confidence interval is:
point estimate +- (critical value)(standard error).
Which is not true of about the margin of error?
...
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
Which is not true about the critical value?
...
Which of the following statements is true with respect to the t-distribution?
#NAME?
To calculate a 95% the confidence interval using the formula, the z-value is always positive and is calculated using which of the following?
z =abs(norm.s.inv(.025)) where abs stands for the absolute value with 2.5% in each tail of the normal distribution.
To calculate a 98% the confidence interval on a mean using the formula where the only a sample standard deviation is given on a sample size (n), the t-value is always positive and is calculated using which of the following?
t =abs(t.inv(.01,n-1)) where abs stands for the absolute value with 1% in each tail of the t-distribution.
If a manager wants to find the desired sample size to stay within a desired margin of error:
-If the population standard deviation is unknown, a sample standard deviation from a pilot sample may be used.
-If n = 45.4, round up to n=46 when collecting the sample.
-The critical value, standard deviation, and desired +-error can be used to calculate
The purpose of a pilot sample is:
to provide an idea of what the population standard deviation might be.
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 / e )^2
FALSE
If a manager believes that the required sample size is too large for a situation in which she desires to estimate the mean income of blue collar workers in a state, which of the following would lead to a reduction in sample size?
-Allow a higher margin of error (increase e)
-Reduce the level of confidence (decrease z-value)
-Somehow reduce the variation in the population (decrease stdev)
The concept of a confidence interval applies directly when estimating a population mean, but is not appropriate when estimating a population proportion.
FALSE
A confidence interval on a proportion is the sample proportion +- critical value * standard error of the proportion.
TRUE
When finding the needed sample size on a proportion, either use the sample proportion or use p = .50 if there isn't a pilot sample.
TRUE
Hypothesis testing is about proving something beyond a reasonable doubt.
TRUE
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.
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.
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: ? ? 80,000
Ha: ? ? 80,000
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: � < 45
Ha: � ? 45
FALSE
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: � ? 25,000
Ha: � > 25,000
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
Ho: � = 16
Ha: � ? 16
If a hypothesis test is conducted for a population mean, a null and alternative hypothesis of the form:
Ho: ? = 100
Ha: � ? 100
will result in a one-tailed hypothesis test since the sample result can fall in only one tail.
FALSE
A two-tailed hypothesis test with alpha = 0.05 is similar to a 95 percent confidence interval.
TRUE
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.
The reason for using the t-distribution in a hypothesis test about the population mean is:
the population standard deviation is unknown.
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
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 believe
Reject Ho if t > 1.729
The test statistic for the mean is the value calculated from the sample using =(xbar-�)/(stdev/sqrt(n).
TRUE
A conclusion to "not reject" the null hypothesis is the same as the decision to "accept" the null hypothesis.
FALSE
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
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 th
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
Box-and-whisker plots are often useful for determining whether one or more populations might be normally distributed.
TRUE
The pooled variance mathematically combines the variances of the two populations and combines it into a single value
TRUE
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 NCAA is interested in estimating the difference in mean number of daily training hours for men and women athletes on college campuses. They want 95 percent confidence and will select a sample of 10 men and 10 women for the study. The sample results ar
TRUE
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
df = 39
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 fo
t-test, assuming unequal variances, where d.f. =complex formula
Under what conditions can the t-distribution be correctly employed to test the difference between two population means?
#NAME?
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.
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 mobi
...
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: �A - �B ? 0
Ha: �A - �B < 0
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
�1 > �2
When conducting a hypothesis test to determine whether or not two groups differ, using paired samples rather than independent samples has the advantage of controlling for sources of variation that might distort the conclusions of the study.
TRUE
In testing for differences between the means of two paired populations, the null hypothesis is:
Ho: ?d=0
Suppose that a group of 10 people join a weight loss program for 3 months. Each? person's weight is recorded at the beginning and at the end of the? 3-month program. To test whether the weight loss program is? effective, the data should be treated? as:
paired samples using the? t-distribution.
The test statistic that is used when testing a null hypothesis for a population variance is the standard normal z-value.
FALSE
When using a chi-square test for the variance of one population, we are assuming that the population is normally distributed.
TRUE
When a hypothesis test is to be conducted regarding a population variance, the test statistic will be:
a ?2 value from the chi-square distribution.
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 currect null and alterhative hypothesis for this test are:
Ho: ?2 ? 2.25
Ha: ?2 > 2.25
If a hypothesis test for a single population variance is to be conducted, which of the following statements is true?
#NAME?
If the variance of the contents of cans of orange juice is significantly more than 0.003, the manager has to order to stop the filling machine. A sample of 26 cans of orange juice showed a standard deviation of 0.06 ounces. Based on the sample and at the
...
The t-distribution is used to test whether two sample variances are equal.
FALSE
A two-tailed test for two population variances could have a null hypothesis like the following: Ho: ?21 = ?22
TRUE
The F-distribution can only have positive values.
TRUE
Which distribution is used in testing the hypotheses about the equality of two population variances?
F-distribution
Which of the following is the appropriate null hypothesis when testing whether two population variances are equal?
Ho: ?1^2 = ?2^2
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
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: ?12 ? ?22
Ha: ?12 = ?22
FALSE
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
Ho: ?A2 ? ?B2
In conducing one-way analysis of variance, the population distributions are assumed normally distributed.
TRUE
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.
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
TRUE
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
Not all population means are equal.
In a one-way analysis of variance test, the following null and alternative hypotheses are appropriate:
Ho: ?1 = ?2 = ?3
Ha: ?1 ? ?2 ? ?3
FALSE
In conducting a one-way analysis of variance where the test statistic is less than the critical value, which of the following is correct?
Conclude that all means are the same and there is no need to conduct the Tukey-Kramer procedure
The one-way ANOVA test involves assuming that the population variances are equal.
TRUE
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; the means are not all the same.
In conducting one-way analysis of variance, the sample size for each group must be equal.
FALSE
In a one-way ANOVA, which of the following is true?
#NAME?
When using the Tukey Kramer procedure, you will need to find the q-value using Appendix I in your textbook.
Employee 1 Employee 2 Employee 3 Employee 4
18 21 14 22
23 22 17 27
15 26 16 23
18 19 21 18
17 24 15 24
Assume we just finished a test to see if th
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
...
In analyzing the relationship between two numeric variables, a scatter plot can be used to detect which of the following?
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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
A correlation coefficient (r) of -0.9 indicates a weak linear relationship between the variables.
FALSE
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 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 ?
?
(rho) when writing Ho
TRUE
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
When the slope in the regression equation is negative, the correlation coefficient (r) will always be negative.
TRUE
The following is Excel Data Analysis output for Regression. The data is comparing the customer satisfaction rating (y) based on the drive thru service time in minutes (x):
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8851
R Square 0.7835
Adjusted R S
The correlation coefficient (r) is -0.8851.
The coefficient of determination (R Square) is always found by taking the correlation coefficient (r) and squaring it.
TRUE
If the coefficient of determination is .45, this can be interpreted as 45% of the variation in the y-variable can be explained by knowing the x-variable.
TRUE
A study comparing package weight (x) to the cost of shipping (y). The Excel Data Analysis Regression output is as follows:
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.90607
R Square 0.820963
Adjusted R Square 0.811017
Standard Error 2.420018
Observa
Approximately 82 percent of the variation in shipping cost (y) can be explained by knowing the package weight (x).
If the R-squared value for a regression model is high, the regression model will necessarily provide accurate forecasts of the y variable.
FALSE
Let's say we conduct a hypothesis test on the regression slope coefficient (r):
Ho: ?=0 (no correlation)Ha: ??0 (is a correlation)
Ho:?=0 (no correlation)
Ha:??0 (is a correlation)
We find that the t-value and p-value are not in the tail and we do not rej
-there is not enough evidence to show there is a linear correlation. With the given the sample size, r is not close enough to 1 or -1 to say there is a linear correlation
-since we can't prove there is a correlation, there is not a predictive equation. We
A regression test was conducted to help in predicting the price of milk in Colorado (y) based on the gasoline prices in Florida (x). The results showed that there was a strong correlation (r=.85). In looking at the analysis a statistician said the results
The correlation is invalid because it is between two seemingly unrelated variables.
The following regression model has been computed based on a sample of twenty observations:
y = 34.2 + 19.3x
Given this model, the predictive model for y when x=40 is 806.2.
TRUE
A regression analysis between sales (Y) and advertising (X) (both in dollars) resulted in the following equation:
y = 100+200x
The above equation implies that an
increase of $10 in advertising is correlated with an increase of $2,000 in sales.
A study was done to see if the cost of the meal (x) could be used to predict the amount tipped (y). A random sample of bills and resulting tips were collected. The smallest bill was $9 and the largest bill was $89 in the sample. The following regression r
-The point estimate for the slope is 0.192.
-We are 95% confident that the true slope is between .158 and .226.
-y = -1.2362 + .1921 * x for values of x between $9 and $89.
The results of a regression analysis indicate:
WeeklySales$(y) = $1242 + $2.32 * Ad$Spent(x)
Is it true that the equation tells us that for every $1 increase in Ad$Spent, the WeeklySales$ increases by $2.32?
TRUE
Given the following sample:
Order Total $(x) Tip Amount $(y)
9.21 1.50
17.82 3.75
25.85 5.00
32.76 6.50
39.43 8.00
47.32 9.00
73.46 15.00
88.45 18.00
Is it okay to use the regression equation for x values smaller than $9 and more than $89?
FALSE
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 joint frequency distribution and contingency analysis can only be completed when the original data is quantitative (numeric data).
FALSE
In Excel a joint frequency distribution table can be created using a tool called PivotTable
TRUE
Joint frequency distributions are used to display:
the number of occurrences at each of the possible joint occurrences of two variables.
The proportions in the joint frequency table can be used to find relative probability for a specified category.
TRUE
Contingency analysis helps to make decisions when multiple proportions are involved.
TRUE
Managers use contingency analysis to determine whether two categorical variables are independent of each other.
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
In a contingency analysis the expected values are based on the assumption that the two variables are independent of each other.
TRUE
An expected cell value of 5 or more is important to ensure an error is not made in the decision making process.
TRUE
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.
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)
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
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
3
2
When the the observed value of one or more cells is less than 5, which of the following is true?
#NAME?
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.
For a chi-square test involving a contingency table, suppose H0 is rejected. We conclude that the two variables are:
related
Given the result of a contingency analysis is to reject Ho and the two categories are found to be dependent:
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