Significance Tests Practice

Situation #1

A university conducts a study to investigate the sleep quality among its students. The researchers are particularly interested in whether the proportion of students who get the recommended 7-9 hours of sleep per night is different from the national average, which is 60%.  They randomly select a sample of 200 students and find that 140 of them report getting the recommended amount of sleep.

Multiple Choice

What is the parameter in this situation?

• p = the true proportion of students at the university who get the recommended amount of sleep

• p = the true mean number of students who get the recommended amount of sleep

• p = the true sleep quality of students

• p = the true proportion of students in the nation that get the recommended amount of sleep

Multiple Choice

We want to perform a significance test at a 5% level of significance to determine if there is evidence to suggest that the proportion of students at this university who get the recommended amount of sleep differs from the national average of 60%.

Which of the following would be the ALTERNATIVE hypothesis for this situation?

• Ha: p = .60

• Ha: p < .60

• Ha: p > .60

• Ha: p ≠ .60

Multiple Select

Which conditions for the test are met? Choose all that apply.

Relevant information: They randomly select a sample of 200 students and find that 140 of them report getting the recommended amount of sleep compared to the national average of 60%

• Random

• 10%

• Large Counts

Multiple Choice

What is the name of the test we should run?

• One sample z interval

• One sample z test

• One sample t interval

• One sample t test

Situation #2

A tutoring center claims that its services lead to an improvement in students' exam scores. To test this claim, a random sample of 15 students who received tutoring is selected. Their exam scores before and after tutoring are recorded. The average difference in scores is calculated to be 6 points with a standard deviation of 12 points.

Multiple Choice

What is the parameter in this situation?

• μ = the true mean improvement in students' exam scores

• μ = the true proportion of improvement in students' exam scores

• μ = the true mean student exam scores

• μ = the true proportion of students whose exam scores increase

Multiple Choice

We want to perform a significance test at a 1% level of significance to determine if there is enough evidence to support the tutoring center's claim of a significant improvement in exam scores.

Which of the following would be the NULL hypothesis for this situation?

• H0: μ = 0

• H0: μ > 0

• H0: μ < 0

• H0: μ ≠ 0

Multiple Select

Which conditions for the test are met? Choose all that apply.

Relevant information: They took a a random sample of 15 students who received tutoring

• Random

• 10%

• Large Sample

Multiple Choice

What is the name of the test we should run?

• One sample z interval

• One sample z test

• One sample t interval

• One sample t test

Situation #3

A high school with about 2000 students is concerned about the amount of time its students spend on smartphones each day. The school believes that more than 70% of its students use smartphones for more than 3 hours daily. To investigate this claim, a random sample of 300 high school students is selected, and it is found that 220 of them use smartphones for more than 3 hours daily.

Multiple Choice

What is the parameter in this situation?

• p = the true proportion of students who use smartphones for more than 3 hours daily

• p = the true mean time students use smartphones daily

• p = the true proportion of time students use smartphones daily

• p = the true mean students who use smartphones more than 3 hours daily

Multiple Choice

We want to perform a significance test at a 1% level of significance to determine if there is sufficient evidence to support the school's concern that more than 70% of its students use smartphones for more than 3 hours daily.

Which of the following would be the ALTERNATIVE hypothesis for this situation?

• Ha: p = .70

• Ha: p < .70

• Ha: p > .70

• Ha: p ≠ .70

Multiple Select

Which conditions for the test are met? Choose all that apply.

Relevant information: A high school with about 2000 students took a random sample of 300 students to compare with a claim of 70% who spent more than 3 hours on smart phones.

• Random

• 10%

• Large Counts

Multiple Choice

What is the name of the test we should run?

• One sample z interval

• One sample z test

• One sample t interval

• One sample t test

Situation #4

A weight loss program claims that participants will lose, on average, 10 pounds after completing the program. To test this claim, a random sample of 30 participants is selected, and their weight loss is recorded after completing the program. The sample mean weight loss is found to be 9 pounds, with a sample standard deviation of 3 pounds.

Multiple Choice

What is the parameter in this situation?

• μ = the true mean weight lost

• μ = the true proportion of weight lost

• μ = the true mean number of people who lost weight

• μ = the true proportion of people who lost weight

Multiple Choice

We want to perform a significance test at a 5% level of significance to determine if there is enough evidence to support the weight loss program's claim of an average weight loss of 10 pounds.

Which of the following would be the NULL hypothesis for this situation?

• H0: μ = 10

• H0: μ > 10

• H0: μ < 10

• H0: μ ≠ 10

Multiple Select

Which conditions for the test are met? Choose all that apply.

Relevant information: They took a a random sample of 30 participants

• Random

• 10%

• Large Sample

Multiple Choice

What is the name of the test we should run?

• One sample z interval

• One sample z test

• One sample t interval

• One sample t test