Matching
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Match the following
words to their correct definitions. Write the correct letter in the space next to the
appropriate definition. (1 point each)
a. | Type I Error | f. | Confidence
Level | b. | Type II Error | g. | Statistical Test | c. | Critical/Rejection Region | h. | Null Hypothesis | d. | Interval
Estimate | i. | Alternative
Hypothesis | e. | Significance level |
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1.
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an interval or a range of values used to estimate
the parameter.
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2.
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the maximum probability of committing a type I
error.
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3.
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the range of values of the test value that
indicates that there is a significant difference and that the null hypothesis should be
rejected.
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4.
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when one does not reject the null hypothesis when
it is false.
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5.
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a statement that there is a difference between a
parameter and some claimed value or that there is a difference between two parameters.
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6.
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the probability an interval contains the
population parameter.
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7.
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when one rejects the null hypothesis when it is
true.
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8.
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a statement that there is no difference between a
parameter and some claimed value or that there is no difference between two
parameters.
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9.
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uses the data obtained from a sample to make
decisions about whether the null hypothesis should be rejected.
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Essay
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10.
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A research organization stated that in 2012 46% of
the Denver metro adult population was single. In a recent random sample of 600 adults, 252 were
single. At á = 0.05, test the claim that the proportion
today is less than in 2012.
a. State the hypothesis and identify the claim. (4
points)
b. Check the conditions for inference and find the critical value(s). (5
points)
c. Compute the test value and corresponding p-value. (5
points)
d. Make a decision to reject or not reject the null hypothesis. (1
point)
e. Summarize your results. (3 points)
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11.
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An exercise physiologist wishes to see whether
a relationship exists between the heart rate (in beats per minute) and minutes spent on a
treadmill. The data are below.
Min on Treadmill, X 20 16
32 24 38 12 8
Heart Rate,
Y
142 120 145
132 150 126
100
a. Compute
the value of the correlation coefficient. (3 points)
b. Find the equation of the regression
line. (3 points)
c. Predict the heart rate for someone spending 35 minutes on the
treadmill. (3 points)
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12.
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The average cost for teeth straightening with
metal braces is approximately $4750. A nationwide franchise thinks that its cost is above that
figure. A random sample of 30 patients across the country had an average cost of $5250 with a
standard deviation of $629. At á = 0.025, can it be concluded that the
mean is more than $4750?
a. State the hypothesis and identify the claim. (4
points)
b. Identify the appropriate test statistic formula to conduct the
hypothesis test (do NOT calculate the test value). (4 points)
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13.
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Nielson Media Research conducted a study on the
duration of hospital stays of children (ages 2-11) and teens (ages 12-17). Based on the sample
statistics below from two independent random samples, is there sufficient evidence to conclude there
is a difference in average hospital stay times between the two groups?
Children Teens
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3.31  = 2.78
 =
0.89  = 0.63
 =
23  = 17
a. Determine a 98% confidence interval
for the true difference in the means. (10 points)
b. Would you reject the null hypothesis that there is not a difference
in the two means based on the above confidence interval? Explain. (4
points)
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14.
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It has been found that the average time
Internet users spend online per week is 18.3 hours. A random sample of 48 teenagers indicated
that their mean amount of Internet time per week was 20.96 hours, and the population variance is 25.6
hours. At the 0.05 level of significance, can it be concluded that the mean time differs from
18.3 hours per week?
a. Suppose the test value
was 1.82, find the corresponding p-value. (4 points)
b. Make the decision to reject or not
reject the null hypothesis based on your p-value in “part a”. Justify your
decision. (4 points)
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15.
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A company institutes
an exercise break for its workers to see if it will improve job satisfaction, as measured by a
questionnaire that assesses worker satisfaction (the higher the score the more satisfied the worker
is). Scores for 10 randomly selected workers before and after the implementation of the
exercise program are shown below. Test the company’s claim at á
= 0.01.
Before 34 28 29 45 26 27 24 15 15 32
After 33 33 45 34 37 41 36 21 20 37
a. State the hypothesis and identify the claim. (4
points)
b. Check the conditions for inference and find the critical value(s). (5
points)
c. Calculate the test statistic and the corresponding p-value. (5
points)
d. Make a decision to reject or not reject the null hypothesis. (1
point)
e. Summarize your results (3 points).
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16.
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The herb ginkgo biloba is commonly used as a
treatment to prevent dementia. In a study of the effectiveness of this treatment, 1545 elderly
subjects were give ginkgo biloba and 1524 elderly subjects were given a placebo. Among those in
the ginkgo treatment group, 212 later developed dementia, and among those in the placebo group, 288
later developed dementia.
a. Find the 99% confidence interval for the difference of the two
proportions. (10 points)
b. Would you reject the null hypothesis
at the 0.01 level of significance (given the above confidence interval) that there is not a
difference in the two proportions? Explain. (4 points)
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17.
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A health care professional wishes to estimate
the birth weights of infants. How large a sample must be obtained if she desires to be 95%
confident that the true mean is within 0.5 ounces of the sample mean? Assume
ó = 8 ounces. (7 points)
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