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# Hypothesis Testing

Item 1: One- tail (upper): Explain the problem you would test for (make up numbers) and state the hypotheses in both numeric and narrative form. Explain why this would be a upper tailed test. Do no calculations or list any formulas.

Item 2: One-tail (lower) Explain the problem you would test for (make up numbers) and state the hypotheses in both numeric and narrative form. Explain why this would be a lower tailed test. Do no calculations or list any formulas.

Item 3: Two- tail: Explain the problem you would test for (make up numbers) and state the hypotheses in both numeric and narrative form. Explain why this would be a upper tailed test. Do no calculations or list any formulas.

Item 4: In a short answer (if possible) explain why the authors state on p. 323: "as the preceding forms show, the equality part of the expression (either >=, <=, or =) always appears in the null hypothesis." Why is this true?

Item 5: What do/may Type I and Type II errors have to do with the type of test you might conduct (upper or lower tail) or the selection of the level of significance?

Item 6: Explain why the phrase "we accept the null hypothesis (Ho) is always is an incorrect statement."

See attached file for full problem description.

#### Solution Preview

Provide 3 examples of each type of hypothesis you will run into: Base examples on production in a factory such as quality assurance

Item 1: One- tail (upper): Explain the problem you would test for (make up numbers) and state the hypotheses in both numeric and narrative form. Explain why this would be an upper tailed test. Do no calculations or list any formulas.

Hypothesis (numeric expression)
H0: &#956; &#8804; 100
Ha: &#956; > 100

Hypothesis (Narrative)
H0: The mean number of items a factory can produce in an hour is less than or equal to 100.
Ha: The mean number of items a factory can produce in an hour is greater than 100.

Explanation
This is a one-tailed test because we're testing if the observed (sample) mean is greater than a given number. (A two-tailed test would determine whether or not the sample mean was not equal to a given number.) It is an upper-tailed test because we're testing if the sample mean is greater than 100, not simply different than 100. We would only reject the null hypothesis if a t-test determined that the sample mean was significantly greater than 100.

Item 2: One-tail (lower): Explain the problem you would test for (make up numbers) and state the hypotheses in both numeric and narrative form. Explain why this would be a lower tailed test. Do no calculations or list any formulas.

Hypothesis (numeric expression)
H0: &#961; &#8805; 0.25
Ha: &#961; < 0.25

Hypothesis (Narrative)
H0: The percentage of factory workers who work overtime hours is greater than or equal to than 25%.
Ha: The percentage of factory workers who work overtime hours is less than 25%.

Explanation
This is a one-tailed test because we're testing if the observed (sample) proportion is less than a given number. (A two-tailed test would determine whether or not the sample proportion was not equal to a given number.) It is an upper-tailed test because we're testing if ...

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