Making a Conclusion Given the Data in Statistics

What is the branch of mathematics dealing with the collection, organization, analysis, interpretation and presentation of data?

• Algebra

• Geometry

• Probability

• Statistics

What is the branch of statistics that involves drawing conclusions about a population based on information contained in a sample taken from that population?

• descriptive statistics

• inferential statistics

• sports statistics

• health statistics

Since populations are often too large, we take a

• sample

• statistic

• data (singular)

• experiment

The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the following school year. She wants to know if each type of food will be equally popular so she can start ordering supplies and making other plans. To find out, she selects a random sample of 100 students and asks them, "Which type of food do you prefer: Asian food, Mexican food, pizza, or hamburgers?" The table shows the data. The P-value for a chi-square test for goodness of fit is 0.0129.  Which of the following is the most appropriate conclusion?

• Because 0.0129 is less than α = 0.05, reject Ho. There is convincing evidence that the food choices are equally popular. 
  

• Because 0.0129 is less than α = 0.05, reject Ho. There is not convincing evidence that the food choices are equally popular. 
  

• Because 0.0129 is less than α = 0.05, reject Ho. There is convincing evidence that the food choices are not equally popular. 
  

• Because 0.0129 is less than α = 0.05, fail to reject Ho. There is not convincing evidence that the food choices are equally popular. 
  

• Because 0.0129 is less than α = 0.05, fail to reject Ho. There is convincing evidence that the food choices are equally popular. 
  

The National Longitudinal Study of Adolescent Health interviewed a random sample of 4877 teens (grades 7 to 12). One question asked was "What do you think are the chances you will be married in the next ten years?" Above is a two-way table of the responses by gender. Which of the following would be the most appropriate type of graph for these data?

• A bar chart showing the marginal distribution of opinion about marriage

• bar chart showing the marginal distribution of gender

• A bar chart showing the conditional distribution of gender for each opinion about marriage

• A bar chart showing the conditional distribution of opinion about marriage for each gender

• Dotplots that display the number in each opinion category for each gender

The National Longitudinal Study of Adolescent Health interviewed a random sample of 4877 teens (grades 7 to 12). One question asked was "What do you think are the chances you will be married in the next ten years?" Above is a two-way table of the responses by gender.

• equal proportions of female and male teenagers are almost certain they will be married in 10 years

• there is no difference between the distributions of female and male teenagers' opinions about marriage in this sample 

• there is no difference between the distributions of female and male teenagers' opinions about marriage in the population

• there is no association between gender and opinion about marriage in the sample

• there is no association between gender and opinion about marriage in the population 

The National Longitudinal Study of Adolescent Health interviewed a random sample of 4877 teens (grades 7 to 12). One question asked was "What do you think are the chances you will be married in the next ten years?" Above is a two-way table of the responses by gender. The expected count of females who respond "almost certain" is

• 487.7 

• 525 

• 965 

• 1038.8 

• 1174 

The National Longitudinal Study of Adolescent Health interviewed a random sample of 4877 teens (grades 7 to 12). One question asked was "What do you think are the chances you will be married in the next ten years?" Above is a two-way table of the responses by gender. The degrees of freedom for the chi-square test for this two-way table are:

• 4

• 8

• 10

• 20

• 4876

The National Longitudinal Study of Adolescent Health interviewed a random sample of 4877 teens (grades 7 to 12). One question asked was "What do you think are the chances you will be married in the next ten years?" Above is a two-way table of the responses by gender. For these data, χ2 = 69.8 with a P-value of approximately 0. Assuming that the researchers used a significance level of 0.05, which of the following is true?

• A type I error is possible 
  

• A type II error is possible 
  

• Both a type I and type II error are possible

• There is no chance of making a type I or type II error because the P-value is approximately 0

• There is no chance of making a type I and type II error because the calculations are correct

A Chi-square goodness-of-fit test is used to test whether a 0 - 9 spinner is “fair” (that is, the outcomes are all equally likely). The spinner is spun 100 times and the results are recorded. The degrees of freedom for the test will be

• 8

• 9

• 10

• 99

• none of these