Introductory Statistics

MA207

Day 11 - Identifying Hypotheses and Errors in Hypothesis Testing

Constructing Hypothesis Tests

Put the following steps in order:

1. Write the alternative hypothesis
2. Create the sampling distribution (using simulation … for now)
3. Gather data
4. Either reject or fail to reject the null hypothesis
5. Write the null hypothesis
6. Decide if your data is extreme

Identify Hypotheses (1)

The average age of first marriage in the U.S. is 28. Does completing college affect this average age? You gather data from 100 randomly selected college graduates who are or have been married and you find the average age of first marriage to be 27.6 years.

Which of these is a correct way to state the null hypothesis? (select all that are correct)

1. H_O = 28
2. H_O: μ=27.6
3. H_O: x=27.6
4. H_O: μ=28
5. H_O: μ<28
6. H_O: College graduates will have the same average first marriage age as non-college graduates.

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Identify Hypotheses (2)

The average age of first marriage in the U.S. is 28. Does completing college affect this average age? You gather data from 100 randomly selected college graduates who are or have been married and you find the average age of first marriage to be 27.6 years.

Which of these is a correct way to state the alternative hypothesis? (select all that are correct)

1. H_A > 28
2. H_A: College graduates have a higher average first marriage age than non graduates.
3. H_A: College graduates have a different average first marriage age than non graduates.
4. H_A: x≠27.6
5. H_A: μ≠28
6. H_A: μ<28

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Identify Hypotheses (3)

According to the National Center for Education Statistics, about 80% of students in the US change their major at least once. Do freshmen entering college with a health science major have a lower chance of changing their major? A random sample of 200 college students who had started as a health science major found that 70% changed their major at least once.

Which of these is a correct way to state the null hypothesis? (select all that are correct)

1. H_O = 80%
2. H_O: μ=160
3. H_O: p=0.8
4. H_O: p=0.7
5. H_O: p=140

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Identify Hypotheses (4)

According to the National Center for Education Statistics, about 80% of students in the US change their major at least once. Do freshmen entering college with a health science major have a lower chance of changing their major? A random sample of 200 college students who had started as a health science major found that 70% changed their major at least once.

Which of these is a correct way to state the alternate hypothesis? (select all that are correct)

1. H_A: p≠140
2. H_A: p≠0.70
3. H_A: p<0.80
4. H_A: p≠0.80
5. H_A: Health science majors have a lower chance of changing their majors than students with other majors

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Errors in Hypothesis Testing

Jury Trial: Null Hypothesis: the person is innocent

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Fill in the blanks with one of the following:

1. Type 1 Error
2. Type 2 Error
3. No Error �

Errors in Hypothesis Testing

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�Fill in the blanks with one of the following:

• Type 1 Error
• Type 2 Error
• No Error

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Question about Errors

1. True or False: It is easier to reject the null hypothesis if the researcher uses a smaller alpha level. Defend your answer.
2. True or False: You are more likely to make a Type I error when using a small sample than when using a large sample. Defend your answer.
3. A gambler is trying to determine if a coin is weighted, but unknown to him the coin is actually fair. He flips the coin 100 times, find the percent heads, and determines that the probability of finding that many heads on a fair coin is 0.04. Using an alpha level of 0.05 does the gambler make an error? If so, what type?