# Multiple Choice Questions Hypothesis Testing-Introduction

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```					                Multiple Choice Questions
Hypothesis Testing - Introduction

1     Testing - Introduction
1. To determine the reliability of experts used in interpreting the results of
polygraph examinations in criminal investigations, 280 cases were studied.
The results were:

True Status
Innocent Guilty
Examiner’s           Innocent             131       15
Decision             Guilty                 9      125

If the hypotheses were H: suspect is innocent vs A: suspect is guilty, then
we could estimate the probability of making a type II error as:

(a) 15/280
(b) 9/280
(c) 15/140
(d) 9/140
(e) 15/146

2. In hypothesis testing, β is the probability of committing an error of Type
II. The power of the test, 1 − β is then:

(a) the probability of rejecting H0 when HA is true
(b) the probability of failing to reject H0 when HA is true
(c) the probability of failing to reject H0 when H0 is true
(d) the probability of rejecting H0 when H0 is true
(e) the probability of failing to reject H0 .

3. In a statistical test of hypothesis, what happens to the rejection region
when α, the level of signiﬁcance, is reduced?

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1   TESTING - INTRODUCTION

(a) The answer depends on the value of β.
(b) The rejection region is reduced in size.
(c) The rejection region is increased in size.
(d) The rejection region is unaltered.
(e) The answer depends on the form of the alternative hypothesis.

4. During the pre-ﬂight check, Pilot Jones discovers a minor problem - a
warning light indicates that the fuel guage may be broken. If Jones decides
to check the fuel level by hand, it will delay the ﬂight by 45 minutes. If
Jones decides to ignore the warning, the aircraft may run out of fuel before
it gets to Gimli. In this situation, what would be:

i)           the appropriate null hypothesis? and;
ii)           a type I error?

(a) Null Hypothesis: assume that the warning can be ignored.
Type I error: decide to check the fuel by hand when there is in fact
enough fuel.
(b) Null Hypothesis: assume that the warning can be ignored.
Type I error: decide to ignore the warning when there is in fact not
enough fuel.
(c) Null Hypothesis: assume that the fuel should be checked by hand.
Type I error: decide to ignore the warning when there is in fact not
enough fuel.
(d) Null Hypothesis: assume that the fuel should be checked by hand.
Type I error: decide to check the fueld by hand when there is in fact
enough fuel.
(e) Null Hypothesis: assume that the aircraft is already late.
Type I error: taking a commercial ﬂight to Gimli in the ﬁrst place.

5. Which of the following is not correct?

(a) The probability of a Type I error is controlled by the selection of the
α level.
(b) The probability of a Type II error is controlled by the sample size.
(c) The power of a test depends upon the sample size and the distance
between the null and alternate hypothesis.
(d) The p-value measures the probability that the null hypothesis is true.
(e) The rejection region is controlled by the α level and the alternate
hypothesis.

6. In testing statistical hypotheses, which of the following statements is false?

c 2006 Carl James Schwarz                  2
1   TESTING - INTRODUCTION

(a) The critical region is the values of the test statistic for which we
reject the null hypothesis.
(b) The level of signiﬁcance is the probability of type I error.
(c) For testing H0 µ = µ0 , HA : µ > µ0 , we reject H0 for high values of
the sample mean X.
(d) In testing H0 : µ = µ0 , HA : µ = µ0 , the critical region is two sided.
(e) The p-value measures the probability that the null hypothesis is true.

7. Since α = probability of Type I error, then 1 − α
(a) Probability of rejecting H0 when H0 is true.
(b) Probability of not rejecting H0 when H0 is true.
(c) Probability of not rejecting H0 when HA is true.
(d) Probability of rejecting H0 when HA is true
(e) 1 − β.
8. Consider the following table in reference to the testing of a null hypothesis:

\$H_0\$    True       \$H_0\$ false
Accept   \$H_0\$             (1)         (2)
Reject   \$H_0\$             (3)         (4)

Which of the following is incorrect?

(a) Entries (1) and (4) are correct decisions.
(b) The P(making entry (2)) is controlled by the sample size for a given
α level.
(c) A Type I error occurs if entry (3) occurs.
(d) Power refers to P(entry (4))
(e) A Type II error occurs when entry (1) is made.

9. In a hypothesis testing problem:

(a) the null hypothesis will not be rejected unless the data are not un-
usual (given that the hypothesis is true).
(b) the null hypothesis will not be rejected unless the p-value indicates
the data are very unusual (given that the hypothesis is true).
(c) the null hypothesis will not be rejected only if the probability of
observing the data provide convincing evidence that it is true.
(d) the null hypothesis is also called the research hypothesis; the alter-
native hypothesis often represents the status quo.
(e) the null hypothesis is the hypothesis that we would like to prove; the
alternative hypothesis is also called the research hypothesis.

c 2006 Carl James Schwarz                  3
1    TESTING - INTRODUCTION

10. A research biologist has carried out an experiment on a random sample
of 15 experimental plots in a ﬁeld. Following the collection of data, a
test of signiﬁcance was conducted under appropriate null and alternative
hypotheses and the P-value was determined to be approximately .03. This
indicates that:

(a) this result is statistically signiﬁcant at the .01 level.
(b) the probability of being wrong in this situation is only .03.
(c) there is some reason to believe that the null hypothesis is incorrect.
(d) if this experiment were repeated 3 per cent of the time we would get
this same result.
(e) the sample is so small that little conﬁdence can be placed on the
result.

11. In a statistical test for the equality of a mean, such as H0 : µ = 10, if
α = 0.05,
(a) 95% of the time we will make an incorrect inference
(b) 5% of the time we will say that there is a real diﬀerence when there
is no diﬀerence
(c) 5% of the time we will say that there is no real diﬀerence when there
is a diﬀerence
(d) 95% of the time the null hypothesis will be correct
(e) 5% of the time we will make a correct inference
12. Which of the following statements is correct?
(a) An extremely small p-value indicates that the actual data diﬀers
markedly from that expected if the null hypothesis were true.
(b) The p-value measures the probability that the hypothesis is true.
(c) The p-value measures the probability of making a Type II error.
(d) The larger the p-value, the stronger the evidence against the null
hypothesis
(e) A large p-value indicates that the data is consistent with the alter-
native hypothesis.

c 2006 Carl James Schwarz                   4

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