Proportion Z Test and Intervals

A credit card company would like to compare the proportion of people who have poor credit to the proportion of people who think they have poor credit. Which of the following is most appropriate?

• 1-Proportion Z-Test

• 1-Mean T-Interval

• 2-Proportion Z-Test

• 2-Mean T-Interval

Which of the following is true pertaining to a 2-proportion z-test?

• The number of successes and failure for each sample do not have to be greater than 10

• A hypothesis test can be calulated even if samples are not random

• The populations should be larger than 10% of the sample sizes

• So long as all conditions are met for one sample, you do not need to check conditions for the other sample

What additional condition must be checked for a 2-proportion test or interval compared to a 1-proportion test or interval?

• You must make sure that the samples are random
• You must make sure that the two samples are independent from one another
• You must make sure that the sum of the samples' sizes are smaller than 10% of the whole population
• The conditions are exactly the same

Null and alternative hypotheses are statements about: 

• population parameters. 
• sample parameters. 
• sample statistics. 
• it depends - sometimes population parameters and sometimes sample statistics. 

In a 2-sample Z or T test the condtions must be met for both samples to proceed.

• True

• False

A sociologist suspects that men are more likely to have received a ticket for speeding than women are. The sociologist wants to sample people and create a two-sample z test to estimate the difference between the proportion of men who have received a speeding ticket and the proportion of women who have received a speeding a ticket.

Which of the following are conditions for this type of hypothesis test?

• They take separate random samples of men and women.

• The samples both include at least 10 people who have received a speeding ticket and least 10 people who haven't.

• The people in each sample can be considered independent.

Rochelle was curious about the gender ratio in mechanical engineering versus chemical engineering in American universities. She obtained separate random samples of 30

students from each field of study. She found that 5 of the mechanical engineering students in her sample were female, and 10 of the chemical engineering students in her sample were female. She plans to use these results to make a two-sample z test to estimate the difference between the proportion of females in each field of study.

What conditions have been met?

• Both samples were randomly selected from their populations.

• The counts of successes and failures are sufficiently large in each sample.

• Individual observations in each sample can be considered independent, and the samples themselves are independent.

Eira works for a consumer advocacy firm. She would like to determine whether there is a difference in the battery life of two different brands of batteries, each of which sells thousands of batteries per year. She obtains separate random samples of 12 batteries from one brand and 20 batteries from the other, then tests the amount of time each battery lasts. There are outliers in her data.

Eira plans to use this information to perform a t test to determine whether there is a difference in the average battery life of the two brands. Assume the population of both battery samples are over 1,000,000.

What conditions have been met?

• Random Condition

• Independence Condition

• Normality Condition

Members of a parenting organization want to use a two-sample t test to determine whether the average tuition for private schools in their state is significantly different for high school students than for elementary students. They plan to take tuition estimates from random samples of 10 schools serving each level.

Which of the following are conditions for this type of test?

• Only sample from schools that include both elementary and high school.

• The tuition estimates in each group are approximately symmetric with no outliers.

• There are approximately equal numbers of private elementary schools and high schools in the state.