Question

Investigators are interested in whether or not a new allergy medication, Allergy-Away, has an effect on the average number of days per year a person reports experiencing allergy symptoms. The mean number of symptomatic days per year reported by the general population of allergy sufferers is 156 with a population standard deviation of 37 days. Investigators collect information from a sample of 64 people on the new medication. They find the mean number of symptomatic days per year reported from their sample is 146.

Conduct a two-tailed hypothesis test (two-tailed z test) on whether or not the population of people taking Allergy-Away have a different mean number of allergy symptomatic days per year (completing the appropriate steps below) than the general population of allergy sufferers, using an alpha (?) level of 0.05.

Part A: Which of the following represents the appropriate null hypothesis (H0), given your research question of interest?

PART A ANSWER: H0:                            [ Select ]                       ["µ < 146", "µ = 146", "µ = 156", "µ < 39", "µ = 64"]      

Part B: Which of the following represents the appropriate alternative hypothesis(H1), given your research question of interest?

PART B ANSWER: H1:                            [ Select ]                       ["µ < 146", "µ ? 0", "µ ? 39", "µ ? 156", "µ ? 64"]      

Part C: Which of the following represents the appropriate critical value(s), testing at an alpha level (?) of 0.05?

PART C ANSWER:                            [ Select ]                       ["-2.67 and 2.67", "-1.96 and 1.96", "-1.65 and 1.65", "-2.78 and 2.78", "-3.22 and 3.22"]      

Part D: What is the z-statistic associated with your test? (rounded to the nearest hundredth)

PART D ANSWER:                             [ Select ]                       ["-2.16", "1.15", "-3.61", "-0.45", "4.82"]      

Part E: What is the p-value associated with your test statistic? (rounded to the nearest ten thousandth)

PART E ANSWER:                             [ Select ]                       ["0.3487", "0.0569", "0.0215", "0.7201", "0.0308"]      

Part F: Given your test results, what is your decision about the null hypothesis?

PART F ANSWER:                             [ Select ]                       ["Reject the null", "Fail to reject (i.e., retain) the null"]      

  

Part G: The best interpretation of the appropriate decision regarding the null hypothesis would be: "Based on our study, we                           

[ Select ]                       ["have", "do NOT have"]      

enough evidence to conclude that the population of people on Allergy-Away appear to have a different mean number of allergy symptomatic days per year than the general population of allergy sufferers."

Answer 1

Part A: Which of the following represents the appropriate null hypothesis (H0), given your research question of interest?

PART A ANSWER: H0: "µ = 156"

Part B: Which of the following represents the appropriate alternative hypothesis(H1), given your research question of interest?

PART B ANSWER: H1: "µ not equal 156 "  

Part C: Which of the following represents the appropriate critical value(s), testing at an alpha level (?) of 0.05?

PART C ANSWER: "-1.96 and 1.96"   

Part D: What is the z-statistic associated with your test? (rounded to the nearest hundredth)

PART D ANSWER: "-2.16"

Part E: What is the p-value associated with your test statistic? (rounded to the nearest ten thousandth)

PART E ANSWER: "0.0308"

Part F: Given your test results, what is your decision about the null hypothesis?

PART F ANSWER:"Reject the null"

  

Part G: The best interpretation of the appropriate decision regarding the null hypothesis would be: "Based on our study, we                           

"have"   

enough evidence to conclude that the population of people on Allergy-Away appear to have a different mean number of allergy symptomatic days per year than the general population of allergy sufferers."