A generic brand of the anti-histamine Diphenhydramine markets a capsule with a 50 milligram dose. The manufacturer is worried that the machine that fills the capsules has come out of calibration and is no longer creating capsules with the appropriate dosage. Research Question: Does the data suggest that the population mean dosage of this brand is different than 50 mg?

  1. (a)  A generic brand of the anti-histamine Diphenhydramine markets a capsule with a 50 milligram dose. The manufacturer is worried that the machine that fills the capsules has come out of calibration and is no longer creating capsules with the appropriate dosage. Research Question: Does the data suggest that the population mean dosage of this brand is different than 50 mg?

    Is this a one-tail test or two tail test? If one tail, state if it is right tail or left tail.

  2. (b)  After receiving complaints from McDonald’s customers in Japan about the amount of french fries being served, the on-line news magazine ”Rocket News” decided to test the actual of the fries served at a particular Japanese McDonald’s restaurant.

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5. (a)

Which of the following cannot be a proper Ha according to my notes (or Hawkes) in9.1 A.Ha :p > 0.50 B.Ha :p < 0.50 C.Ha :p = 0.50 D.Ha:p ̸= 0.50

According to the Rocket News article, the official weight standard set by McDonald’s of Japan is for a medium sized fries to weigh 120 grams. The publication weighed the fries from 25 different medium fries they purchased and found the average weight of the fries in their sample to be 115 grams with variance of 100 grams. Research Question: Does the data suggest that the medium fries from this McDonald’s in Japan are underpacked? Use α =0.05.

I computed TS correctly and it is Z = -2.5. Based upon the guidelines in 9.5, this TS leads to reject H0 . Now suppose I change α = 0.01, does the conclusion lead to accept H0 ?

(c) About 10% of the human population is left-handed. A researcher at Penn State speculates that students in the College of Arts and Architecture are more likely to be left-handed than people in the general population. A random sample of 100 students in the College of Arts and Architecture is obtained and 18 of these students were found to be left-handed. Research Question: Are artists more likely to be left-handed than people in the general population?

Is this a one-tail test or two tail test? If one tail, state if it is right tail or left tail.

  1. (d)  Sarah works for the Urban Pollination Project at UW. Five years ago, 25% of urban gardens were visited by native bees, and Sarah would like to show that this proportion is low now than it was five years ago. Suppose Sarah collects data and calculates a p-value of 0.089.

    Should Sarah reject H0 with α = 0.05?

  2. (e)  Sarah works for the Urban Pollination Project at UW. Five years ago, 25% of urban gardens were visited by native bees, and Sarah would like to show that this proportion is different now than it was five years ago. In the previous part, Sarah’s p-value is 0.089. Does it change now or remains the same?

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