Deck 17: An Alternative to Hypothesis Testing: Confidence Intervals

Question 1

The national norm for third graders on a standardized test of reading achievement is a score of 27. Mrs. Johnson obtains the mean score on the test for a random sampling of third graders from her school district. The results for Mrs. Johnson's sample are $\overline{X} = 33.1, s_X = 5.2 and n=30$ (a) Construct the 95% confidence interval for her population mean score. (b) Construct the 99% confidence interval for her population mean score. (c) What generalization is illustrated by a comparison of the answers to (a) and (b)?

Answer 1

(a)

(b)

(c) the higher the level of confidence, the wider the interval

Question 2

A random sample of 20 students at Alpha College is asked how many hours a week they study on the average. The following are the results:

and

Construct the 95% confidence interval for the mean hours studied per week for the entire student body. What does the 95% refer to? Be very explicit and precise in your answer.

Answer 2

If the study were repeated many times, 95% of the intervals constructed in the same way would include

.

Question 3

The directors of a charitable organization wish to compare the effectiveness of two programs for training their phone solicitors. Thirty-one volunteers are randomly divided into two groups. Group A is trained using method A and Group B using method B. The following are the results for this year's fund drive (in dollars per volunteer):

Answer 3

Question 4

The following are the achievement test results for 15 matched pairs taught by Method A and Method B.
(a)Construct the 95% confidence interval for $(\mu_A - \mu_B)$ .
(b)Ignore thecorrelation coefficient and treat the two samples as though they were independent. Construct the 95% confidence interval for $(\mu_A - \mu_B)$ .
(c)What does a comparison of the answers to (a) and (b) suggest concerning the effect on interval estimates of using samples?

Question 5

Random samples are selected and the 95% confidence interval for is constructed. It runs from -3.1 to 9.4.
(a) If a two-tailed test were used at would a significant difference be found between and Explain.
(b) Give the 95% confidence interval for

Question 6

Determine the 95% confidence interval for in each of the following cases:
a) b) c) d) A comparison of the widths of the intervals obtained in (a), (b), and (c) suggests what generalization concerning the sampling variation of the correlation coefficient?

Question 7

Which statement is true?

A) Any problem in hypothesis testing could be handled through estimation
B) Any problem in estimation could be handled through hypothesis testing
C) Hypothesis testing and estimation are mutually interchangeable
D) Hypothesis testing and estimation are never interchangeable

Question 8

Confidence intervals of a parameter are preferred over hypothesis testing when

A) great accuracy is required
B) logic does not point to a possible value of the parameter that is of special interest
C) we know the parameter's value and wish to predict sample outcomes
D) sampling is not random

Question 9

Which statement, if any, is incorrect?

A) confidence intervals are preferred over point estimation because they are more likely to be correct
B) the population value to be estimated does not vary, but confidence intervals made from different samples will vary
C) once a confidence interval is constructed, it is no longer proper to speak of the probability that it includes the population value
D) all of the above are true

Question 10

The rule for constructing a confidence interval of the population mean is

A)
B)
C)
D)

Question 11

Confidence intervals are generally to be preferred over point estimates because confidence intervals

A) have a firmer statistical basis
B) result in greater precision
C) account for sampling error
D) are based on more degrees of freedom

Question 12

For a random sample of 100 cases,
and

. The 95% confidence interval for

would run approximately from

A) 143 to 157
B) 131 to 169
C) 147 to 153
D) 138 to 162

Question 13

We construct a 90% confidence interval for P, the population proportion of freshmen able to pass a proposed English placement exam. The sample interval runs from .43 to .49. This tells us that

A) there is a 90% probability that P falls between .43 and .49
B) there is a 90% probability that an interval so constructed will include P
C) 90% of the time P will fall between .43 and .49
D) 90% of intervals so constructed will fall between .43 and .49

Question 14

Which set of circumstances is most likely to result in a narrow confidence interval?

A) large n and a confidence level of .95
B) large n and a confidence level of .99
C) small n and a confidence level of .95
D) small n and a confidence level of .99

Question 15

For a confidence interval of
, an interval of lesser width results

A) when n is smaller
B) when is larger
C) when a larger value of C (the confidence coefficient) is required
D) in none of the above circumstances

Question 16

The advantage of expressing a confidence interval in terms of the number of standard deviations of the variable is that

A) it is more precise
B) normal curve theory will then apply
C) it compensates for the fact that the importance of a given interscore distance depends on the size of the standard deviation of the variable
D) all of the above will occur

Question 17

The rule for constructing a confidence interval of the difference between two means is

A)
B)
C)
D)

Question 18

In establishing a confidence interval for the difference between two means, selecting a confidence level of .95 rather than a confidence level of .90 implies that

A) we can be less sure that the interval contains the true difference
B) the interval will be wider
C) the difference between the two sample means will be less
D) the difference between the two population means will be greater

Question 19

Which factor will not affect the width of a confidence interval constructed to estimate the difference between two population means?

A)
B) the size of S_X and S_Y
C) the size of n_X and n_Y
D) the level of confidence

Question 20

A 95% confidence interval for
runs from -2 to +6. From this we can infer that

A) is probably greater than
B) is probably greater than
C) there may be no difference at all between and
D) the difference between and is not very large in any case

Question 21

Suppose a 95% confidence interval for
runs from -10 to -2. It appears likely that

A)
B)
C)
D) none of the above

Question 22

If we wish to estimate
or

within given limits, the required sample size will be related to

A) the magnitude of the standard deviation(s)
B) the confidence coefficient
C) both of the above
D) neither of the above

Question 23

Suppose a 95% confidence interval for
runs from -5 to +2. If

were tested against a two-tailed alternative hypothesis using

our decision about

A) is uncertain
B) should be to reject
C) should be to retain
D) cannot be determined without further information

Question 24

Suppose a 95% confidence interval for
runs from -10 to -2. If

were tested against a two-tailed alternative hypothesis using

our decision about

A) is uncertain
B) should be to reject
C) should be to retain
D) cannot be determined without further information

Question 25

Suppose a 95% confidence interval for
runs from 48 to 56. If we had tested

against

using

we would

A) have rejected
B) have retained
C) not be able to decide about unless n were known
D) not be able to decide about unless n and were known

Question 26

The practice of making confidence intervals of
is recommended because

A) it is more accurate than hypothesis testing
B) it does not require the assumption of a normal bivariate distribution
C) it calls attention more directly to the influence of sampling variation on r
D) it takes better account of the number of degrees of freedom involved

Question 27

A confidence interval for
is highly preferable to a point estimate when

A) n is small
B) n is large
C) r is small
D) is large

Question 28

A 95% confidence interval for
is computed for sample results. The interval runs from -.75 to +.25. This suggests that

A) is probably negative
B) a small sample was used
C) a computational error was made
D) r is significant