Download 1 - UC Davis Statistics

1 The discharge of suspended solids from a phosphate mine is normally distributed, with
a mean daily discharge of 27 milligrams per liter (mg/l) and a standard deviation of 14
mg/l. What proportion of days will the daily discharge exceed 50 mg/l?
_________
2 A used-car dealership has found that the length of time before a major repair is
required on the cars it sells is normally distributed, with a mean equal to 10 months and
a standard deviation of 3 months. If the dealer wants only 5% of the cars to fail before
the end of the guarantee period, for how many months should the cars be guaranteed?
_________ months
3 Due to a variation in laboratory techniques, impurities in materials, and other unknown
factors, the results of an experiment in a chemistry laboratory will not always yield the
same numerical answer. In an electrolysis experiment, a class measured the amount of
copper precipitated from a saturated solution of copper sulfate over a 30-minute period.
The n = 30 students calculated a sample mean and standard deviation equal to 0.145
and 0.0051 mole, respectively. Find a 90% confidence interval for the mean amount of
copper precipitated from the solution over a 30-minute period.
_________
4 Assume a two-tailed test with z = 3.01 and = 0.05. Complete the following:
p-value: _________
Conclusion: _________________
Assume an upper one-tailed test with z = 2.47 and = 0.05. Complete the following:
p-value: _________
Conclusion: _________________
Assume a two-tailed test with z = -1.30 and = 0.01. Complete the following:
p-value: _________
Conclusion: _________________
Assume a lower one-tailed test with z = -2.88 and = 0.01. Complete the following:
p-value: _________
Conclusion: _________________
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5 The braking ability was compared for two 2005 automobile models. Random samples
of 64 automobiles were tested for each type. The recorded measurement was the
distance (in feet) required to stop when the brakes were applied at 40 miles per hour.
These are the computed sample means and variances:
Do the data provide sufficient evidence to indicate a difference between the mean
stopping distances for the two models?
Test statistic = _________
p-value = _________
Conclusion: _________________
Interpretation: _________________
6 The variability in a scientist’s measuring equipment was observed for a random sample
of 26 test runs from a normal distribution. The sample yielded a variance of 33.
Estimate the population variance using a 95% confidence interval. (use a separate
sheet to answer if necessary)
7 Two soft drink machines dispense liquids of 10 ounces, on the average. The question
is whether the two machines are equally consistent (i.e., equally variable) in the
dispensing of the liquid. To answer this question, a sample of size 10 was obtained
from each machine and the sample standard deviations were computed to be
= 1.87
ounces and
= 1.25 ounces. Perform the appropriate test for equality of variances
using = 0.05. (use a separate sheet to answer if necessary)
8 Set up the rejection regions for the following testing conditions. Assume the
assumptions of normality and equal variances are satisfied.
a.
= 10,
= 12, and = 0.05.
b.
= 4,
= 8, and = 0.01.
c.
= 15,
= 15, and = 0.05.
(use a separate sheet to answer if necessary)
9 An experiment was conducted to study the relationship between the ratings of a
tobacco leaf grader and the moisture content of the tobacco leaves. Twelve leaves
were rated by the grader on a scale of 1 to 10, and corresponding readings of moisture
content were made.
Calculate rs. Do the data provide sufficient evidence to indicate an association between
the grader’s ratings and the moisture contents of the leaves?
Test statistic = _________
Critical Value(s) = _________
Conclusion: _________________
Interpretation: _________________
10 A university investigation was conducted to determine whether women and men
complete medical school in significantly different amounts of time, on the average. Two
independent random samples were selected and the following summary information
concerning times to completion of medical school computed:
Women
Men
Sample Size
90
100
Sample Mean
8.4 years 8.5 years
Sample Standard Deviation 0.6 years 0.5 years
a.
Perform the appropriate test of hypothesis to determine whether there is a
significant difference in time to completion of medical school between women
and men. Test using
.
b.
Find the p-value associated with the test in part (a).
(use a separate sheet to answer if necessary)
11 The Environmental Protection Agency wanted to compare the proportion of plants in
violation of air quality standards for two different industries: steel and utility. Two
independent samples of plants were selected and monitored. The following data was
recorded:
Steel: n1 = 150 Number of violations = x1 = 12
Utility: n2 = 160 Number of violations = x2 = 12
a.
Set up the appropriate null and alternative hypotheses.
b.
Compute the value of the test statistic.
c.
Set up the appropriate rejection region for a = 0.01.
d.
What is the appropriate conclusion?
(use a separate sheet to answer if necessary)
12 Let m denote the true average delivery time of a letter from a specific carrier. For a
large-sample z test of
: m = 3 versus
m  ¹ 3, find the p-value associated with
each of the given values of the test statistic, and state whether each p-value will lead to
a rejection of the null hypothesis when performing a level 0.05 test.
a.
b.
c.
d.
e.
(use a separate sheet to answer if necessary)
13 A random sample of 150 observations was selected from a binomial population, and 87
successes were observed. Do the data provide sufficient evidence to indicate that the
population proportion p is greater than 0.5? Use the critical value approach and the pvalue approach. (use a separate sheet to answer if necessary)
14 Suppose that a t-test is being conducted at the 0.05 level of significance to test
versus
. A sample of size 20 is randomly selected. The rejection
region is:
a. t > 1.725
b. t < -1.729
c. t > -2.093
d. t < 2.086
15 In testing the hypotheses
, the following information is known:
n = 64, = 78, and = 10. The test statistic is equal to:
a. +1.96
b. +2.4
c. -2.4
d. –1.96
16 Which of the following p-values will lead us to reject the null hypothesis if the level of
significance
0.05?
a. 0.025
b. 0.05
c. 0.10
d. 0.20
17 For an F distribution, the number of degrees of freedom for the denominator
a.
must be larger than the number of degrees of freedom for the numerator
b.
must be equal to the number of degrees of freedom for the numerator
c.
must be smaller than the number of degrees of freedom for the
numerator
d.
can be larger, smaller, or equal to the number of degrees of freedom for
the numerator
18 If a sample has 15 observations and a 95% confidence estimate for
constructed, the appropriate t-score is 2.131
True
False
need to be
19 Given the significance level 0.05, the F-value for the degrees of freedom
= 8, is 4.82.
=5 and
True
False
20 In a regression problem the following pairs of (x, y) are given: (4,1), (4,-1), (4,0), (4,-2)
and (4,2). That indicates that:
a.
The correlation coefficient is –1
b.
The correlation coefficient is 0
c.
The correlation coefficient is 1
d.
The coefficient of determination is between –2 and 2
21 In a simple linear regression problem, the least squares line is = 2.73 - 1.02 , and
the coefficient of determination is 0.7744. The correlation coefficient must be –0.88.
True
False