Test 1 Professor Colson
Fall 2004
1. Suppose that there are exactly two bags, Bag A and Bag B. Each bag contains 50 equal-sized tokens inscribed with a dollar value. The frequency table for each bag is as follows:
Bag A Bag B
Value Frequency Value Frequency
2 14 2 1
4 13 4 1
6 11 6 1
8 4 8 2
10 3 10 3
12 2 12 4
14 1 14 11
16 1 16 13
18 1 18 14
Furthermore, suppose that one of these two bags is presented to you with the claim that the bag is bag A. You must judge (decide) the probable truth of the claim statistically by randomly selecting one token from the given bag and using the p-value approach. Assume that you have selected a voucher inscribed with $14.
a.) What are the two hypotheses?
Ho: Bag presented is Bag A
H1: Bag presented is Bag B
b.) What is the direction of extreme?
To the right
c.) What is the numerical value for the p-value?
3/50 = 0.06
d.) If the level of significance alpha is set at 10%, is the $14 voucher statistically significant?
yes
e.) If the level of significance alpha is set at 5%, is the $14 voucher statistically significant?
no
2. Claude manages a plant that manufactures light bulbs. Claude is interested in finding out the average lifetime of a new model of a 100-watt light bulb that he is producing. The average lifetime for the population of 100-watt light bulbs produced by his competitor is about 40 hours. Claude wishes to test whether the average lifetime for his new model bulbs is greater than that of his competition on average.
a.) What is the population under study?
The light bulb plant
b.) State the hypotheses to be tested.
Ho: mean is equal to 40
H1: mean is greater than 40
c.) The manufacturer decides to test his theory at a level of alpha equal 0.10. What is the chance of making a Type I error? What about a Type II error?
0.10; can�t tell about the type II error.
d.) He conducts a statistical test and the data was not statistically significant at the alpha equal 0.10 level. Give a possible p-value for this test.
0.15; in general, anything greater than to 0.10.
3. Referring to the famous President Clinton-Monica Lewinsky scandal, a poll stated that 59% of those surveyed said that President Clinton should resign if he lied. This result was based on a poll of 1537 adults surveyed.
a.) How many adults surveyed feel President Clinton should resign if he lied?
59% * 1537 = 906.83 = 907
b.) Suppose that a listing of the residential homes in the Washington, D.C. area was available. A simple random sample of homes was obtained and all of the adults residing at the selected homes were surveyed. What type of sampling technique is described?
Cluster sampling
c.) Adults residing in apartment complexes would not have had a chance to be included in the survey. What type of bias is this?
Selection bias
4. The key difference between a controlled experiment and an observational study is that in a controlled experiment:
a.) treatments are assigned to subjects.
b.) response bias is smaller.
c.) inference is used when results are not observed.
d.) there are no confounding variables.
5. In cluster sampling, the chance that any unit is selected depends on the size of the clusters.
a.) True
b.) False
6. a.) What percentage of data does the IQR contain inside of it?
50% of the data because Q3 is the 75th percentile and Q1 is the 25th percentile.
b.) What type of bias does a mail survey usually result in and why?
Non-response bias
7. It was reported that a study was double-blinded. Clearly explain what double-blinded means in your own words.
Double blinded refers to a study in which the subjects and those conducting the experiment do not know who is receiving the treatment or the placebo.