Question

For the next 8 questions, choose the test which is applicable and enter the capital letter corresponding to that test in the space provided. If no test discussed in STAT263 is applicable, enter the letter W. If more than one test is appropriate, you need only state one for full marks.

A) Z test about μ
B) t test about μ
C) χ² test about σ or σ²
D) pooled-variance t test
E) Z test about μ₁ & μ₂
F) F test about σ₁ & σ₂ or σ₁² & σ₂²
G) t test about (rho) ρ
H) Z test about p₁ & p₂
I) Z test about σ or σ²
J) paired data t test
K) paired data Z test
L) Z test about p (proportion)
M) χ² test, goodness of fit
N) ANOVA, μ₁, μ₂, .., μ_k
O) ANOVA, regression
P) t test about β (slope)
Q) Sign test (paired data)
R) Sign test (one sample)
S) χ² test for contingency table
T) Bartlett’s test  
U) U test
V) Welch’s Approximate t test
W) no test is appropriate

28. The proportion of drivers who use a seat belt in a state that does not have a mandatory seat belt law is claimed. An advertising campaign was conducted to increase this proportion. Two months after the campaign, 104 out of a random sample of 590 drivers were wearing seat belts. Was the campaign successful? Choose the test which is applicable and enter the capital lettercorresponding to that test in the space provided.

29. A tanning studio claims that the tan produced by using their studio is better than that produced by a tanning lotion. To investigate this claim 20 volunteers were randomly assigned to use the tanning studio for 3 days or to use the tanning lotion and then each volunteer’s tan was evaluated on a scale from 1 to 5 by a judge who did not know what method the volunteer had used. The data cannot be assumed normally distributed. Is there evidence to support the studio’s claim? Choose the test which is applicable and enter the capital letter corresponding to that test in the space provided.

30. A die (one of a pair of dice) is rolled 120 times to try to determine if it is a fair die. A fair die is one in which all surfaces are equally likely to appear. Does the data summarized in the table below suggest the die is not fair?

Choose the test which is applicable and enter the capital letter corresponding to that test in the space provided.

31. A sample of 15 serum amylase determinations (units/100 ml) was drawn from a normally distributed population. The sample yielded a mean of 96.0 and a standard deviation of 34.8. Is there evidence to conclude that the variance of the underlying population is greater than 1200? Choose the test which is applicable and enter the capital letter corresponding to that test in the space provided.

32. Random samples of n₁ = 13 and n₂ = 15 are taken from two normally distributed populations. The researcher wishes to determine if there is a difference in means. An F test with H_A: σ ₁ ≠ σ ₂ is performed and the p-value is found to be 0.31. Choose the test which is applicable and enter the capital letter corresponding to that test in the space provided.

33. In an experiment to investigate whether cell phone use increases a driver’s reaction time, 100 students were randomly assigned to 1) a cell phone group (CP) or 2) a control group (C). The reaction times (in milliseconds) to a light which flashed at irregular times was recorded for both groups: _CP = 583.7, s_CP = 88.3, _C = 533.7,s_C = 65.3. If the data can be assumed to come from normally distributed populations, what test could be used to see if is there evidence that the cell phone use increased driver reaction times? Choose the test which is applicable and enter the capital letter corresponding to that test in the space provided.

34. When it is operating correctly, a machine manufacturing tennis balls produces balls with a mean weight of 57.6 g.   The last eight balls manufactured weighed: 57.8, 57.4, 57.2, 57.1, 57.0, 57.3, 57.2, 57.1. If the data can be assumed to be normally distributed, does this suggest the machine is not operating correctly? Choose the test which is applicable and enter the capital letter corresponding to that test in the space provided.

35. A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for 24 randomly selected subjects are recorded. A lower score indicates less pain. The "before" value is matched to an "after" value and the differences are calculated. The differences are normally distributed. Did hypnotism reduce pain? Choose the test which is applicable and enter the capital letter corresponding to that test in the space provided.

Answer 1

QUESTION 28.

Here the aim of the test is to see whether the proportion of drivers who use a seat belt in a state that does not have a mandatory seat belt law. This is a Z test about p and hence option L is correct.

QUESTION 29.

Here the aim of the test is to see whether the tan produced by the tanning studio is better than the tanning lotion or not and here it cannot be assumed that the data is normally distributed. This is a U test and hence option U is correct.

QUESTION 30.

Here the aim of the test is to see whether the die is fair or not i.e. whether the proportion of heads and tails in the die are equally likely or not. This is a Z test about p and hence option L is correct.

QUESTION 31.

Here the aim of the test is to see whether the variance of the population is greater than 1200 or not This is a test about and hence option C is correct.

QUESTION 32.

Here the aim of the test is to test the difference of means. As the p-value of the F test of is more than 0.05, it can be concluded at 5% level of significance that the variance are not equal. This is a Welch's Approximate t test and hence option V is correct.

QUESTION 33.

Here the aim of the test is to see whether the cell phone use increases a driver’s reaction time or not This is a test for contigency table and hence option S is correct.

QUESTION 34.

Here the aim of the test is to see whether the mean weight of the tennis balls matches with the claimed weight or not This is a t test about and hence option B is correct.

QUESTION 35.

Here the aim of the test is to see whether hypnotism reduce pain or not This is a sign test (paired data) and hence option Q is correct.

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