Significance Tests and Decision Making

A medical experiment compared the herb Echinacea with a placebo for preventing colds. The study used 50 different response variables usually associated with colds, such as low-grade fever, congestion, frequency of coughing, etc. The subjects were 40 women between 25 and 40 years of age. One response variable was “volume of nasal secretions” (if you have a cold, you blow your nose a lot). Take the average volume of nasal secretions in people without colds to be µ = 1. An increase to µ = 3 indicates a cold. Which of the following describes the significance level of a test of H0: µ=1 versus Ha: µ>1?

• The probability that the test rejects H0 when µ = 1 is true

• The probability that the test rejects H0 when µ = 3 is true.

• The probability that the test fails to reject H0 when µ = 3 is true.

• The probability that the test fails to reject H0 when µ = 1 is true

• None of the above

The water diet requires you to drink two cups of water every half hour from the time you get up until you go to bed, but otherwise allows you to eat whatever you like. Four adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The weights (in pounds) are (in photo). Which of the following conditions must be met in order to use a t-procedure on these paired data?

• Only the distribution of pre-diet weights must be approximately Normal.

• Only the distribution of differences (after 6 weeks – before) must be approximately Normal.

• The distribution of both pre-diet weights and six-week weights must be approximately Normal.

• The distribution of pre-diet weights and the distribution of differences (after 6 weeks – before)

  must be approximately Normal.

• All three distributions—before diet, after 6 weeks, and the difference—must be approximately Normal.

What is the statistical method used in making decisions using experimental data?

• Simple analysis

• Hypothesis testing

• Analytical testing

• Experimental testing

What level which describes the probability of committing an incorrect decision about the null hypothesis?

• Level of error

• Level of acceptance

• Level of hypothesis

• Level of significance

Which of the following describes an alternative hypothesis using two-tailed test?

• 𝐻𝑎 = 100

• 𝐻𝑎 > 100

• 𝐻𝑎 ≠ 100

• 𝐻𝑎 < 100

Which of the following would be an appropriate null hypothesis?

• The mean of a sample is equal to 75

• The mean of a population is equal to 75

• The mean of a sample is not equal to 75

• The mean of a population is greater than 75

Which of the following must be used as the significance level if we want a lower possibility of correct decision?

• 1 %

• 2 %

• 5 %

• 10 %

When is a Type I error committed?

• We reject a null hypothesis that is true

• We reject a null hypothesis that is false

• We fail to reject a null hypothesis that is true

• We fail to reject a null hypothesis that is false

If the t-computed value is 2.430 and the critical value is 2.011, what will be the decision?

• Reject the null hypothesis

• Support the null hypothesis

• Reject the alternative hypothesis

• Do not reject the null hypothesis

Before the opening of classes, parents were asked to answer a survey. Those in favor of alternative learning mode were 1,900 out of 5,000 randomly selected parents. Using α = 0.10 level, is there enough evidence to conclude that the percentage of parents who are in favor of alternative learning mode is less than 50%? What is the appropriate alternative hypothesis?

• Ha : p > 0.50

• Ha : p < 0.50

• Ha : p = 0.50

• Ha : p ≠ 0.50