Question 1

In a beer consumption study,a researcher makes an assumption that males will consume more beer per week than females; this can be stated in a:

Accepted Answer

The assumption that males will consume more beer per week than females is a statement that can be tested through research, thus making it a hypothesis.

Question 2

Which of the following is the first step in hypothesis testing?

Accepted Answer

The first step in hypothesis testing is to state the null hypothesis and alternative hypothesis. This sets up the framework for the rest of the testing process, allowing for the selection of an appropriate test statistic and the development of a decision rule. Only after these steps can the test statistic be calculated and a conclusion reached.

Question 3

Which of the following is not a step in hypothesis testing?

Accepted Answer

Evaluating the randomness of the sample is not a step in hypothesis testing. The steps in hypothesis testing are: stating null and alternative hypotheses, choosing the appropriate statistical test, collecting data and calculating test statistics, determining the p-value and comparing it to the significance level, and making a decision and interpreting the results.

Question 4

What type of data would be necessary to have when testing for differences in means?

Accepted Answer

To test for differences in means, the data must be continuous and measurable, or metric. Nominal and ordinal data are categorical and do not have numerical values that can be compared for means.

Question 5

Samples in which the measurement of a variable in one population may influence the measurement of the variable in the other are called:

Accepted Answer

The answer of Samples in which the measurement of a...

Question 6

When do you say the difference between two numbers is statistically significant?

Accepted Answer

Statistically significant difference means that the difference between two numbers is unlikely to have occurred by chance or sampling error. This is determined by conducting hypothesis testing with a chosen level of significance (usually 0.05 or 0.01). The size of the difference or the length of time it is observed may not necessarily make it statistically significant; it depends on the level of variability and sample size in the data.

Question 7

Suppose in our sample results we find that males average drinking five soft drinks per week,compared with six soft drinks per week for females.In the absence of additional analysis,what type of difference has been illustrated?

Accepted Answer

The difference illustrated is a mathematical difference because it is based purely on the arithmetic calculation of the average number of soft drinks consumed by males and females per week, without any statistical analysis or consideration of the significance or importance of the difference.

Question 8

The hypothesis of the status quo is typically referred to as the ______________ hypothesis.

Accepted Answer

The hypothesis of the status quo is usually referred to as the null hypothesis, which assumes that there is no significant difference between two groups or variables being compared. It is often used as the default hypothesis unless there is strong evidence to support an alternative hypothesis.

Question 9

What is the meaning of testing a hypothesis at an alpha level of 0.05?

Accepted Answer

The answer of What is the meaning of testing a...

Question 10

What is the purpose of hypothesis testing?

Accepted Answer

Hypothesis testing is used to determine whether there is enough evidence to draw conclusions about some characteristics of the population based on the sample data. It involves making a null hypothesis and an alternative hypothesis, collecting data, and evaluating the probability of obtaining the observed results assuming the null hypothesis is true. Based on this probability, a decision is made to either reject or fail to reject the null hypothesis, which helps to draw conclusions about the population characteristics.

Question 11

Why is the null hypothesis called the hypothesis of the status quo?

Accepted Answer

The null hypothesis is called the hypothesis of the status quo because it assumes no significant difference or relationship between the variables being tested. It is the default assumption and will only be rejected if there is convincing evidence that the alternative hypothesis is true. Therefore, it maintains the "status quo" of no effect or relationship until proven otherwise by the data.

Question 12

For comparing means,most statistical software packages use which test?

Accepted Answer

The t-test is the appropriate test for comparing means. It is used when comparing the means of two groups, while ANOVA is used when comparing the means of three or more groups. Chi-square is used for categorical data, while beta is a probability distribution used for modeling continuous data between 0 and 1.

Question 13

In testing a hypothesis about means,if the sample size was less than 30,then the appropriate statistical test would be?

Accepted Answer

If the sample size is less than 30, the appropriate statistical test would be the t-test. The z-test assumes that the data is normally distributed with a standard deviation known, while the t-test allows for the estimation of the standard deviation from the sample data, making it more appropriate for smaller sample sizes. The chi-square test is for testing associations between categorical variables, while ANOVA is for testing differences between means of more than two groups. Cross-tabulation is a method for analyzing categorical data.

Question 14

In most statistical software packages,the t-test is often substituted for which test statistic?

Accepted Answer

The t-test is often substituted for the z-test when the sample size is small or the population standard deviation is unknown, as both tests assess the mean of a population but under different conditions.

Question 15

What kind of error is being made if the researcher fails to reject the null hypothesis when it is,in fact,false?

Accepted Answer

Failing to reject the null hypothesis when it is actually false is a type II error.

Question 16

What is the purpose of statistical inferences?

Accepted Answer

The purpose of statistical inferences is to make generalizations about population characteristics from sample results.

Answer: E
 Statistical inferences serve multiple purposes, including making generalizations about population characteristics from sample results, estimating mean, median, mode, variance, and skewness of large sample data, studying characteristics of binomial or Poisson random variables, and fully describing the characteristics of the population.

Question 17

A market researcher is trying to determine whether males differ from females with regard to the following question: Do you drink soft drinks? Which of the following tests would be most appropriate?

Accepted Answer

The chi-square test would be the most appropriate test to determine whether there is a significant difference between the proportion of males and females who drink soft drinks. This is a categorical variable with two groups (males and females), and the chi-square test can assess whether there is a significant association between them.

Question 18

Which of the following is the appropriate statistical test when examining cross tabulations?

Accepted Answer

The appropriate statistical test for examining cross tabulations is chi-square test. It is used to determine whether there is a significant association or correlation between two categorical variables.

Question 19

The exact probability of getting a computed test statistic that was largely due to chance is referred to as the______________.

Accepted Answer

The p-value is the exact probability of getting a computed test statistic that is due to chance. It helps determine the statistical significance of a result and whether it can be attributed to chance or not. The chi-square value, z-test value, median value, and t-test value are all measures used in different types of statistical tests, but only the p-value relates to the probability of chance.

Question 20

A researcher is interested in comparing product rating scores between males and females.By drawing a sample of males and a sample of females,the researcher needs to find a statistical test that applies to____________.

Accepted Answer

The researcher is comparing two separate samples of males and females, therefore it is appropriate to use a statistical test that applies to independent samples. Examples of such tests include the independent samples t-test or the Mann-Whitney U test. Dependent samples would refer to data collected from the same individuals before and after a treatment, and convenience samples refer to samples that are easily accessible but may not be representative of the population of interest.

Quiz 16: Statistical Testing of Differences and Relationships