Statistics 200: Lab Activity for Section 4.1 Introducing hypothesis tests - Lear
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Statistics 200: Lab Activity for Section 4.1
Introducing hypothesis tests - Learning objectives:
Recognize when and why statistical tests are needed
Specify null and alternative hypotheses based on a question of interest, defining relevant parameters
Recognize that hypothesis tests examine whether sample data provide sufficient evidence to refute the null hypothesis and support the alternative hypothesis
Compare the strength of evidence that different samples have about the same hypothesis
Activity 1: Writing hypotheses
Write down the hypotheses for the test in each case below (use proper notation):
Does the proportion of people who support gun control differ between males and females?
H0:
Ha:
Is the average hours of sleep per night for college students less than 7?
H0:
Ha:
Is there evidence that the mean of group A is not the same as the mean of group B?
H0:
Ha:
Is there a negative correlation between hours per week spent studying and number of parties attended per week?
H0:
Ha:
Activity 2: Statistical test or confidence interval?
In each of the scenarios below, indicate a) whether the researchers should use a statistical test or confidence interval, and b) what the population parameter(s) of interest is/are.
Polling 1000 people in a large community to determine the average number of hours a day people watch television.
Testing 100 high school freshman and 100 high school seniors on the same algebra test to determine if there is evidence for the claim that seniors score higher.
Testing 50 people in a driving simulator to find the average reaction time to hit the brakes when an object is seen in the view ahead.
Activity 3: Evidence for the claim.
You will need to use the data in the Minitab Express file “Hypothetical Data for Section 4.1 Lab” for this activity. The file is available in Canvas.
We are interested in testing to see if there is evidence that the population mean for mathematics placement test scores is greater than 25.
Write the correct null and alternative hypotheses for this situation:
H0:
Ha:
The data for four hypothetical samples is included in the Minitab Express data set. Create summaries, either numerical or graphical, to evaluate which of the samples provides the most or least amount of evidence against the null and for the alternative.
What kind of summaries did you create?
Which of these samples provides the most evidence for the alternative hypothesis?
Which of these samples provides the least evidence for the alternative hypothesis?
Researchers in a hypothetical town are trying to see if there is evidence that an upcoming ballot measure for a tax increase will pass with more than 50% of the vote.
Write the correct null and alternative hypotheses for this situation:
H0:
Ha:
They take four hypothetical samples of the same size and record whether individuals will vote ‘yes’ or ‘no’. Their hypothetical data is included in the same dataset you used for the above question. Again, use these data to decide which of the samples provides the most or least amount of evidence against the null and for the alternative.
What kind of summaries did you create?
Which of these samples provides the most evidence for the alternative hypothesis?
Which of these samples provides the least evidence for the alternative hypothesis?
We are interested in testing to see if there is evidence that the correlation between test grades (in percentages) and hours spent playing video games is negative for a population of students.
Write the correct null and alternative hypotheses for this situation:
H0:
Ha:
Below are four scatterplots of hypothetical samples collected to investigate the claim:
Which of these samples provides the most evidence for the alternative hypothesis?
Which of these samples provides the least evidence for the alternative hypothesis?
Activity 4: Key words.
What are key words or phrases that help you decide if the alternative hypothesis includes a >, <, or a ?
Explanation / Answer
Activity 1: Writing hypotheses
Write down the hypotheses for the test in each case below (use proper notation):
Does the proportion of people who support gun control differ between males and females?
H0: Proportion of males who support gun control is same as proportion of female who support gun control. pmale = pfemale
Ha:Proportion of males who support gun control is different from proportion of female who support gun control. pmale pfemale
Is the average hours of sleep per night for college students less than 7?
H0: AVerage hours of sleep per night for college students is a least 7 hours. = 7 hours
Ha: Average hours of sleep per night for college students is less than7 hours. < 7 hours
Is there evidence that the mean of group A is not the same as the mean of group B?
H0: Mean of group A is equal to mean of group B. A = B
Ha:Mean of group A is not equal to mean of group B. A B
Is there a negative correlation between hours per week spent studying and number of parties attended per week?
H0: There is no correlation betweenhours per week spent studying and number of parties attended per week. r = 0
Ha: There is egative correlation betweenhours per week spent studying and number of parties attended per week. r < 0
Activity 2: Statistical test or confidence interval?
(a) Polling 1000 people in a large community to determine the average number of hours a day people watch television.
Confidence Interval must be used
(2) Testing 100 high school freshman and 100 high school seniors on the same algebra test to determine if there is evidence for the claim that seniors score higher.
Statistical Test is used. (as two samples for compariosn is given)
(3) Testing 50 people in a driving simulator to find the average reaction time to hit the brakes when an object is seen in the view ahead.
Confidence interval should be used
Activity 3: Evidence for the claim.
We are interested in testing to see if there is evidence that the population mean for mathematics placement test scores is greater than 25.
Write the correct null and alternative hypotheses for this situation:
H0 : mean for mathematics placement test scores is less than or equal to 25. = 25
Ha : mean for mathematics placement test scores is greater than 25. > 25
Researchers in a hypothetical town are trying to see if there is evidence that an upcoming ballot measure for a tax increase will pass with more than 50% of the vote.
Write the correct null and alternative hypotheses for this situation:
H0: Ballot measure for a tax increase will not pass with more than 50% of the vote. p = 0.50
Ha: Ballot measure for a tax increase will not pass with more than 50% of the vote. p > 0.50
We are interested in testing to see if there is evidence that the correlation between test grades (in percentages) and hours spent playing video games is negative for a population of students.
Write the correct null and alternative hypotheses for this situation:
H0: CORR(Test Grades , Hours spend video games) = 0
Ha:CORR(Test Grades , Hours spend video games) < 0
Activity 4: Key words.
Key words or phrases that are important are "at least" "more than", "less than" , "greater than" "not equal to" " different" etc.
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