Question 1

A researcher calculates a chi-square test statistic of 8.56.At a = .05 and n= 3,the critical value of the chi-square statistic is 7.81.What is the appropriate statistical conclusion?
A)Reject the null hypothesis
B)Can't determine;not enough information given
C)Fail to reject the null hypothesis
D)Reject the alternative hypothesis
E)Conclude that the null hypothesis is true

Accepted Answer

The calculated chi-square test statistic (8.56) is greater than the critical value of chi-square statistic (7.81) at a significance level of α=0.05 and degrees of freedom n-1=2. Therefore, we can reject the null hypothesis and accept the alternative hypothesis.

Question 2

A clothing manufacturer traditionally makes sweatshirts from three different fabrics: A,B and C.Over the years,the percentages sold of each fabric were 50,35,and 15,respectively.Recently,the manufacturer began producing running suits from the same three fabrics.During the first three months of production,the company received orders for 6,500 suits made from fabric A,3,400 from fabric B,and 2,700 from fabric C.What is the appropriate test to determine whether sales results of the new running suit are similar to what would be expected given the previous sales history of sweatshirts made of the three fabrics?
A)Regression analysis
B)z-test for comparing sample mean against a standard
C)Chi-square test
D)z-test for comparing sample proportion against a standard
E)None of these are correct.

Accepted Answer

The appropriate test to determine whether sales results of the new running suits are similar to what would be expected given the previous sales history of sweatshirts made of the three fabrics is the chi-square test. This test is used for comparing observed frequencies to expected frequencies and determining whether they are significantly different. In this case, we can calculate the expected frequencies by multiplying the total number of running suits by the percentage of each fabric sold historically. Then, we can compare these expected frequencies to the actual frequencies for each fabric using the chi-square test.

Question 3

A clothing manufacturer traditionally makes sweatshirts from three different fabrics: A,B and C.Over the years,the percentages sold of each fabric were 50,35,and 15,respectively.Recently,the manufacturer began producing running suits from the same three fabrics.During the first three months of production,the company received orders for 6,500 suits made from fabric A,3,400 from fabric B,and 2,700 from fabric C.What would be the expected number of running suits made of fabric B sold during the first three months based on past years' sales results of sweatshirts?
A)3,500
B)1,190
C)4,410
D)4,500
E)None of these are correct.

Accepted Answer

The expected number of running suits made from fabric B is calculated by applying the same percentage of fabric B used in sweatshirts (35%) to the total number of running suits ordered (6,500 + 3,400 + 2,700 = 12,600). Thus, 0.35 * 12,600 = 4,410.

Question 4

Which of the following statements is TRUE with respect to outliers?
A)They represent special cases that should be treated differently from the rest of the observations.
B)They can be located using frequency analysis.
C)They can have a very strong influence on the sample mean.
D)All of these are correct.
E)None of these are correct.

Accepted Answer

Outliers are indeed special cases that often require different treatment, can be identified through methods like frequency analysis, and can significantly influence measures of central tendency like the mean, making all the provided statements true.

Question 5

The population mean is hypothesized to be 200.The sample mean (x-bar)is 220.The sample size (n)is 25.The sample standard deviation (s)is 15.The estimated value of the standard error of the mean is
A)2.6.
B)3.0.
C)1.6.
D)0.6.
E)0.9.

Accepted Answer

The answer of The population mean is hypothesized to be...

Question 6

The population mean is hypothesized to be 200.The sample mean (x-bar)is 220.The sample size (n)is 25.The sample standard deviation (s)is 15.The degrees of freedom would equal
A)14.
B)24.
C)219.
D)199.
E)Cannot tell from the given information

Accepted Answer

To calculate the degrees of freedom for a t-test, we use the formula: df=n-1, where n is the sample size. Therefore, in this case, df = 25-1 = 24.

Question 7

Because ____ and ____ measures are similar when it comes to analysis,many researchers refer to both types as continuous measures.
A)interval,ratio
B)nominal,interval
C)ordinal,ratio
D)nominal,ordinal
E)ratio,nominal

Accepted Answer

Interval and ratio measures are similar in that they both provide numerical data that can be analyzed using descriptive and inferential statistics. Nominal and ordinal measures, on the other hand, cannot be analyzed in the same way because they do not have a consistent scale. Therefore, A is the best choice because it correctly identifies the two types of measures that are similar in analysis.

Question 8

Which of the following statements concerning confidence intervals is FALSE?
A)A confidence interval can be inferred when a probabilistic sample is drawn.
B)A confidence interval is produced by calculating the degree of nonsampling error for the particular statistic.
C)Precision can be increased by increasing sample size or decreasing the confidence level.
D)A narrower confidence interval can be obtained by increasing the sample size.
E)A narrower confidence interval can be obtained by decreasing the degree of confidence desired.

Accepted Answer

Confidence intervals are calculated based on sampling error, not nonsampling error. Nonsampling errors are errors not related to the act of sampling itself, such as measurement errors or data processing errors, and are not accounted for in the calculation of confidence intervals.

Question 9

Which of the following is FALSE about the use of percentages when reporting results?
A)Unless decimals have a special purpose,they should be omitted.
B)Percentages should be rounded to whole numbers.
C)Decimals may convey greater accuracy than the figures can support.
D)It is unnecessary and redundant to include percentages along with the raw count for frequency analyses.
E)All of these statements are true concerning the use of percentages when reporting results.

Accepted Answer

Including percentages along with the raw count for frequency analyses can provide additional information about the distribution of the data and is not unnecessary or redundant.

Question 10

For which of the following types of measures does the mean NOT provide a meaningful value?
A)Ratio
B)Equal-interval scales
C)Interval
D)Ordinal
E)Continuous measures

Accepted Answer

The mean does not provide a meaningful value for ordinal measures, as they only represent a ranking or ordering of values and not a true quantitative difference between them.

Question 11

The confidence interval is
A)a measure of the variation in responses for continuous measures.
B)the level of error related to the probability of rejecting the null hypothesis.
C)a counting of the number of cases that fall into the various response categories.
D)a projection of the range within which a population parameter will lie at a given level of confidence based on a statistic obtained from an appropriately drawn sample.
E)the arithmetic mean value across all responses for a variable.

Accepted Answer

A confidence interval is a range of values that are likely to contain the true value of a population parameter. It is based on a statistic obtained from a sample and takes into account the variability of the data. The level of confidence reflects the probability that the interval contains the true population parameter.

Question 12

A researcher had calculated the sample chi-square test statistic to be equal to |2 = 7.71.For an alpha level of 0.10 and 4 degrees of freedom,the critical value of the chi-square statistic is 7.78.The appropriate conclusion is that the
A)sample result is likely to be attributed to chance alone.
B)null hypothesis should not be rejected.
C)null hypothesis should be rejected.
D)Both a and b are correct.
E)The alternative hypothesis is true.

Accepted Answer

The answer of A researcher had calculated the sample chi-square...

Question 13

The population mean is hypothesized to be 200.The sample mean (x-bar)is 220.The sample size (n)is 25.The sample standard deviation (s)is 15.The median split for this sample is
A)100.
B)110.
C)200.
D)220.
E)There is not enough information to determine the median split.

Accepted Answer

The median split refers to dividing a dataset into two equal parts based on the median value, not the mean or any other statistical measure provided. The information given does not include data distribution or individual data points, making it impossible to determine the median or the median split.

Question 14

Converting from continuous to categorical measures
A)results in loss of information about a variable.
B)works because higher levels of measurement have all the properties of lower levels of measurement.
C)in many cases is really useful for interpreting the results.
D)is a process that really isn't subject to a lot of rules.
E)All of these are correct.

Accepted Answer

Converting from continuous to categorical measures indeed results in a loss of information because the precise values are grouped into broader categories. This process is based on the principle that higher levels of measurement include the properties of lower levels, allowing for such conversion. It can be useful for interpreting results, as categorical data may be easier to analyze and understand in certain contexts. Lastly, while there are guidelines for converting continuous data to categorical data, the process can be flexible and dependent on the specific goals of the analysis, indicating that it isn't strictly ruled.

Question 15

When it comes to standard deviations,if everyone were basically the same on some characteristic or felt the same way about some topic or object,the standard deviation would be
A)very small.
B)difficult,if not impossible,to calculate.
C)very large.
D)None of these are correct.
E)very small and difficult to calculate.

Accepted Answer

If everyone were basically the same on some characteristic or felt the same way about some topic or object, there would be little variation in the data set. This would result in a very small standard deviation.

Question 16

Which of the following statements concerning the sample standard deviation is FALSE?
A)Sample standard deviation is a measure of the variation in responses.
B)Analysts reporting descriptive statistics for continuous measures should always report standard deviations along with mean values.
C)Standard deviation is meaningful and appropriate only for interval- and nominal-level measures.
D)An analyst must be aware of the concerns of spurious precision when reporting standard deviations.
E)Outliers can have a marked effect the calculation of a standard deviation.

Accepted Answer

Standard deviation is meaningful and appropriate for interval- and ratio-level measures, not nominal-level measures.

Question 17

A clothing manufacturer traditionally makes sweatshirts from three different fabrics: A,B and C.Over the years,the percentages sold of each fabric were 50,35,and 15,respectively.Recently,the manufacturer began producing running suits from the same three fabrics.During the first three months of production,the company received orders for 6,500 suits made from fabric A,3,400 from fabric B,and 2,700 from fabric C.What is the value of the test statistic useful for determining how well the pattern of sales (by fabric type)of the new running suit corresponds to the expected pattern?
A)136.21
B)584.81
C)0.973
D)422.13
E)None of these are correct.

Accepted Answer

To determine how well the pattern of sales of the new running suit corresponds to the expected pattern, we need to use the chi-squared goodness of fit test.

The formula for the test statistic is: 
χ² = Σ[(Observed frequency - Expected frequency)²/Expected frequency]

We can fill in the values:
χ² = [(6500 - (0.5*12700))²/(0.5*12700)] + [(3400 - (0.35*12700))²/(0.35*12700)] + [(2700 - (0.15*12700))²/(0.15*12700)]
χ² = 584.81

Therefore, the value of the test statistic is 584.81. The correct answer is (B).

Question 18

Descriptive statistics include all of the following measures EXCEPT
A)median.
B)confidence intervals.
C)skewness.
D)variance.
E)range.

Accepted Answer

Descriptive statistics include measures such as median, skewness, variance, and range, but do not include confidence intervals, which are a type of inferential statistic used to estimate population parameters.

Question 19

To calculate sampling error for a proportion,which of the following pieces of information is NOT needed?
A)The z-score representing the desired degree of confidence
B)The number of valid cases overall for the proportion
C)The sample standard deviation
D)The relevant proportion obtained from the sample
E)All of these are relevant and necessary pieces of information for the calculation of sampling error for a proportion.

Accepted Answer

The sample standard deviation is not necessary for the calculation of sampling error for a proportion. The relevant pieces of information are the z-score representing the desired degree of confidence, the number of valid cases overall for the proportion, and the proportion obtained from the sample.

Question 20

Which of the following statements about mean values is NOT true?
A)Mean values can be calculated for any variable in a data set.
B)Mean values are only meaningful for continuous measures.
C)Mean values should be presented with several decimals to improve their precision.
D)The mean is only useful with equal-interval scales.
E)Outliers can have a very strong influence on a sample mean.

Accepted Answer

It is not necessary to present mean values with several decimals, as this can lead to a false sense of precision. The appropriate number of decimals to include depends on the context and level of precision needed for the analysis or interpretation.

Quiz 17: Analysis and Interpretation: Individual Variables Independently

A researcher calculates a chi-square test statistic of 8.56.At a = .05 and n= 3,the critical value of the chi-square statistic is 7.81.What is the appropriate statistical conclusion?

Which of the following statements is TRUE with respect to outliers?

The population mean is hypothesized to be 200.The sample mean (x-bar) is 220.The sample size (n) is 25.The sample standard deviation (s) is 15.The estimated value of the standard error of the mean is

The population mean is hypothesized to be 200.The sample mean (x-bar) is 220.The sample size (n) is 25.The sample standard deviation (s) is 15.The degrees of freedom would equal

Because and measures are similar when it comes to analysis,many researchers refer to both types as continuous measures.

Which of the following statements concerning confidence intervals is FALSE?

Which of the following is FALSE about the use of percentages when reporting results?

For which of the following types of measures does the mean NOT provide a meaningful value?

The confidence interval is

A researcher had calculated the sample chi-square test statistic to be equal to |2 = 7.71.For an alpha level of 0.10 and 4 degrees of freedom,the critical value of the chi-square statistic is 7.78.The appropriate conclusion is that the

The population mean is hypothesized to be 200.The sample mean (x-bar) is 220.The sample size (n) is 25.The sample standard deviation (s) is 15.The median split for this sample is

Converting from continuous to categorical measures

When it comes to standard deviations,if everyone were basically the same on some characteristic or felt the same way about some topic or object,the standard deviation would be

Which of the following statements concerning the sample standard deviation is FALSE?

Descriptive statistics include all of the following measures EXCEPT

To calculate sampling error for a proportion,which of the following pieces of information is NOT needed?

Which of the following statements about mean values is NOT true?