Type I and II Error and Power of the Test

When leaving for school on an overcast morning, you make a judgment on the null hypothesis: The weather will remain dry. What would the results be of Type I and Type II errors?

• Type I Error: carry an umbrella and it rains

  Type II Error: carry no umbrella, but weather remains dry

• Type I Error: get drenched

  Type II Error: carry no umbrella, but weather remains dry

• Type I Error: get drenched

  Type II Error: carry an umbrella, and it rains

• Type I Error: get drenched

  Type II Error: needlessly carry around an umbrella

• Type I Error: needlessly carry around an umbrella

  Type II Error: get drenched

Which of the following is incorrect?

• The power of a test concerns its ability to detect a true alternative hypothesis.

• The significance level of a test is the probability of rejecting a true null hypothesis.

• The probability of a Type I Error plus the probability of a Type II error always equals 1.

• Power equals 1 minus the probability of failing to reject a false null hypothesis.

• Anything that makes a null hypothesis harder to reject increases the probability of committing a Type II Error.

Suppose Ho: p = 0.40, Ha: p < 0.40, and against the alternative p = 0.30, the power is 0.80. Which of the following is a valid conclusion?

• The probability of committing a Type I error is 0.10.

• If p = 0.30 is true, the probability of failing to reject Ho is 0.20.

• The probability of committing a Type II error is 0.70.

• All of the above are valid conclusions.

• None of the above are valid conclusions.

Which of the following is a true statement?

• A Type I error is a conditional probability.

• A Type II Error results if one incorrectly assumes the data are normally distributed.

• Types I and II errors are caused by mistakes, however small, by the person conducting the test.

• In conducting a hypothesis test, it is possible to make both a Type I and Type II error simultaneously.

Which of the following statements is incorrect?

• The significance level of a test is the probability of a Type II error.

• Given a particular alternative, the power of the test against that alternative is 1 minus the probability of the Type II error associated with that alternative.

• If the significance level remains fixed, increasing the sample size reduces the probability of a Type II error.

• If the significance level remains fixed, increasing the sample size raises the power.

• With the sample size held fixed, increasing the significance level decreases the probability of a Type II error.

If all other variables remain constant, which of the following will not increase the power of a hypothesis test?

• Increasing the sample size.

• Increasing the significance level.

• Increasing the probability of a Type II error.

• Decreased variability in the data.

• An increased difference between the true and the hypothesized parameters.

A company that produces bungee cords continually monitors the strength of the cords. If the mean strength from a sample drops below a specified level, the production process is halted and the machinery inspected. Which of the following would result from a Type I error?

• Halting the production process when sufficient customer complaints are received.

• Halting the production process when the bungee cord strength is below specifications.

• Halting the production process when the bungee cord strength is within specifications.

• Allowing the production process to continue when the bungee cord strength is below specifications.

• Allowing the production process to continue when the bungee cord strength is within specifications.

Given that the power of a significance test against a particular alternative is 97 percent, which of the following is true?

• The probability of mistakenly rejecting a true null hypothesis is less than 3 percent.

• The probability of mistakenly rejecting a true null hypothesis is 3 percent.

• The probability of mistakenly rejecting a true null hypothesis is greater than 3 percent.

• The probability of mistakenly failing to reject the false null hypothesis is 3 percent.

• The probability of mistakenly failing to reject the false null hypothesis is different from 3 percent.

A Human Resource manager suspects that employees are abusing the company's sick day policy and plans to investigate this issue. The hypotheses under consideration are the following:

H_o: employees are not abusing the company's sick day policy

H_a: employees are abusing the policy by taking sick days when they are not actually sick

What is the power of the test?

• The probability of mistakenly accusing employees of abusing the sick day policy when in fact they aren't abusing the policy.

• The probability of mistakenly not accusing employees who are abusing the sick day policy.

• The probability of correctly not accusing employees who are not abusing the sick day policy.

• The probability of correctly accusing employees who are abusing the sick day policy.

• The probability that the test will come to a correct decision on whether or not employees are abusing the sick day policy.

A hypothesis test is to be performed at a significance level of α = 0.10. What is the effect on the probability of committing a Type I error if the sample size is increased?

• The probability of committing a Type I error decreases.

• The probability of committing a Type I error increases.

• The probability of committing a Type I error remains the same.

• This cannot be determined without knowing the relevant standard deviation.

• This cannot be determined without knowing if a Type II error is committed.