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Understanding Statistical Inference – M
Homework #5

20 points

Instructions: Answer each question fully. Show your work for all questions since partial credit
may be given for incorrect answers. You may use your book and notes for assistance. However,
you must complete each homework assignment individually WITHOUT the assistance of
anyone else, including your clasmates. If you cannot answer the question in the alloted space,
please attach a separate piece of paper. Good luck!

1. Many companies that manufacture lightbulbs advertise their 60-watt bulbs as having an
average burn time of 1000 hours. A cynical consumer bought 30 bulbs and burned them until
they failed. He found that they burned for an average of M = 1233, with a standard deviation
of s = 232.06. Perform all six steps of hypothesis testing to determine whether the burn time
of lightbulbs differs from that claimed by companies manufacturing them.

2. As quality control manager at a raisin manufacturing and packaging plant, you want to ensure
that all the boxes of raisins you sell are comparable, with 30 raisins in each box. In the plant,
raisins are poured into boxes until the box reaches its sale weight. To determine whether a
similar number of raisins are poured into each box, you randomly sample 36 boxes about to
leave the plant and count the number of raisins in each. You find the mean number of raisins
in each box to be 29.86, with s = 3.87. Perform the six steps of hypothesis testing to
determine whether the average number of raisins per box differs from the expected 30.

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3. (Table: TV and Aggressiveness) In a fictional study, a pretest-posttest design was used to
examine the influence of a television program on children’s aggressiveness. The number of
aggressive responses was measured during an observation period both before and after the
television program. Perform the six steps of hypothesis testing using the following data to
determine if there is a difference in the number of aggressive behaviors in children after having
viewed the television program.

Table: TV and Aggressiveness

Participant Before After
1 6 9
2 4 3
3 12 11
4 9 12
5 10 14
6 2 6
7 14 12

4. Dr. Johnson, a psychologist and researcher, was interested in assessing whether stress
affects health. He measured student stress levels immediately after exposure to two
stressors. The first stressor was spontaneous bursts of loud noise. The second stressor
involved asking students to give an extemporaneous speech in front of the other participants.
Stress levels were measured by asking students to complete brief self-report measures of
stress immediately after exposure to the two stress conditions. Dr. Johnson hypothesized
that students would report higher stress after the public speaking stressor compared to the
noise stressors. Can Dr. Johnson use a t test to test his hypothesis? Why or why not?

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