Download Rayna Todorcheva 1154MATH330-002 Assignment Homework8

Rayna Todorcheva
Assignment Homework8-week 9 due 10/27/2015 at 12:15pm EDT
4. (1 pt) A polling organization has been hired to conduct
a survey to determine the proportion of people who are likely
to support an upcoming ballot initiative. To help determine the
size of the sample required for the main poll, a preliminary poll
of 20 people is taken that yields the results below. (Yes indicates
that the person will support the initiative, No indicates that they
won’t.)
1. (1 pt) Suppose that a sample has been drawn from a normal population to conduct the hypothesis test
H0 : σ2 = 30
H1 : σ2 > 30
Assume that you know that the sample variance is s2 = 51,
the sample size is n = 23, and take α = 0.02. Draw the sampling
distribution, and use it to determine each of the following:
A. The value of the standardized test statistic:
Note: For the next part, your answer should use interval notation. An answer of the form (−∞, a) is expressed (-infty, a), an
answer of the form (b, ∞) is expressed (b, infty), and an answer
of the form (−∞, a) ∪ (b, ∞) is expressed (-infty, a)U(b, infty).
B. The rejection region for the standardized test statistic:
No
No
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
Yes
No
Yes
No
Correct Answers:
A. Do Not Reject H1 .
B. Reject H1 .
C. Do Not Reject H0 .
D. Reject H0 .
• 1755
5. (1 pt)
Which of the following statements is not correct for an Fdistribution?
Correct Answers:
•
•
•
•
Yes
No
Yes
No
Based on the results of the peliminary poll, how large a sample is required for the main poll, assuming that the main poll
should have a margin of error of 2.7% and a confidence level of
97.7%.
Sample Size =
C. The p-value is
D. Your decision for the hypothesis test:
•
•
•
•
1154MATH330-002
37.4
(37.6595,infinity)
0.0213721
C
• A. Degrees of freedom for the denominator are always
smaller than the degrees of freedom for the numerator
• B. Exact shape of the distribution is determined by two
numbers of degrees of freedom
• C. Degrees of freedom for the numerator can be larger,
smaller, or equal to the degrees of freedom for the denominator.
• D. Variables that are F-distributed range from 0 to 100
2. (1 pt) The sample mean and standard deviation from a random sample of 26 observations from a normal population were
computed as x̄ = 36 and s = 12. Calculate the t statistic of the
test required to determine whether there is enough evidence to
infer at the 7% significance level that the population mean is
greater than 32.
Test Statistic =
In testing the difference between two population means using two independent samples, the sampling distribution of the
sample mean difference x̄1 − x̄2 is normal if the:
Correct Answers:
• A. populations are non-normal and the sample sizes are
large
• B. populations are normal
• C. sample sizes are both greater than 30
• D. all of the above are required conditions
• 1.69967317119759
3. (1 pt) The hypothesis test
H0 : µ = 22
H1 : µ 6= 22
is to be carried out. A random sample is selected, and yields
x̄ = 24 and s = 6. If the value of the t statistic is t =
1.37436854187255, what is the sample size? (If rounding is
required, round to the nearest integer.)
Sample Size =
Correct Answers:
• A
• B
6. (1 pt)
A medical statistician wants to estimate the average weight
loss of people who are on a new diet plan. In a preliminary
study, he guesses that the standard deviation of the population
of weight loss is about 12 pounds. How large a sample should
Correct Answers:
• 17
1
he take to estimate the mean weight loss to within 2 pounds,
with 90% confidence?
Sample Size =
Correct Answers:
• (18.9569546289297,27.0430453710703)
Correct Answers:
10. (1 pt) For the data set
• 98
(−2, −2), (3, 3), (6, 4), (7, 7), (9, 11),
7. (1 pt)
One of the few negative side effects of quitting smoking is
weight gain. Suppose that the weight gain in the 12 months
following a cessation in smoking is normally distributed with a
standard deviation of 8 pounds. To estimate the mean weight
gain, a random sample of 50 quitters was drawn and the sample
mean was found to be 26 pounds. Determine the 97% confidence interval estimate of the mean 12-month weight gain for
all quitters.
Note: For each confidence interval, enter your answer in the
form (LCL, UCL). You must include the parentheses and the
comma between the confidence limits.
Confidence Interval =
carry out the hypothesis test
H0 β1 = 1
H1 β1 6= 1
Determine the value of the test statistic and the associated
p-value.
Test Statistic =
p-Value =
Correct Answers:
• 0.443290593424157
• 0.687576
11. (1 pt)
Whenever the null hypothesis is not rejected, the alternative
hypothesis:
Correct Answers:
• (23.5448234323438,28.4551765676562)
•
•
•
•
8. (1 pt)
A statistics practitioner took a random sample of 47 observations from a population whose standard deviation is 21 and
computed the sample mean to be 110.
Note: For each confidence interval, enter your answer in the
form (LCL, UCL). You must include the parentheses and the
comma between the confidence limits.
A. Estimate the population mean with 95% confidence.
Confidence Interval =
B. Estimate the population mean with 95% confidence, assuming a sample size of 17.
Confidence Interval =
C. Estimate the population mean with 95% confidence, assuming a sample size of 380.
Confidence Interval =
A Type II error is defined as:
•
•
•
•
• B
• D
12. (1 pt)
Using the confidence interval when conducting a two-tail test
for the population mean µ, we do not reject the null hypothesis
if the hypothesized value for µ:
• (103.996310939499,116.003689060501)
• (100.017423208547,119.982576791453)
• (107.888576640128,112.111423359872)
• A. falls in the rejection region
• B. is the to the left of the lower confidence limit (LCL)
• C. falls between the lower confidence limit (LCL) and
the upper confidence limit (UCL)
• D. is the the right of the upper confidence limit (UCL)
9. (1 pt)
How many rounds of golf do those physicians who play golf
play per year? A survey of 12 physicians revealed the following
numbers:
38,
18,
3,
32,
37,
18,
16,
15,
29,
12,
A. rejecting a true null hypothesis
B. rejecting a false null hypothesis
C. not rejecting a true null hypothesis
D. not rejecting a false null hypothesis
Correct Answers:
Correct Answers:
5,
A. must be modified
B. is rejected
C. is not rejected
D. is true
Which of the following p−values will lead us to reject the
null hypothesis if the level of significance equals 0.05?
53
Estimate with 92% confidence the mean number of rounds
played per year by physicians, assuming that the population is
normally distributed with a standard deviation of 8.
Note: For each confidence interval, enter your answer in the
form (LCL, UCL). You must include the parentheses and the
comma between the confidence limits.
Confidence Interval =
•
•
•
•
A. 0.055
B. 0.10
C. 0.15
D. 0.025
Correct Answers:
• C
• D
2
13. (1 pt) A dean in the business school claims that GMAT
scores of applicants to the school’s MBA program have increased during the past 5 years. Five years ago, the mean and
standard deviation of GMAT scores of MBA applicants were
520 and 45, respectively. 25 applications for this year’s program were randomly selected and the GMAT scores recorded.
If we assume that the distribution of GMAT scores of this year’s
applicants is the same as that of 5 years ago, find the probability
of erroneously concluding that there is not enough evidence to
supports the claim when, in fact, the true mean GMAT score is
550. Assume α is 0.02.
P(Type II Error) =
16. (1 pt) Determine β for the following test of hypothesis,
given that µ = 47.
H0 : µ = 54
H1 : µ < 54
For this test, take σ = 12, n = 39, and α = 0.05.
P(Type II Error) =
Correct Answers:
• 0.0228547787823123
17. (1 pt) For the data set
(−2, −2), (2, 3), (5, 4), (9, 7), (11, 8),
carry out the hypothesis test
H0 β1 = 0
H1 β1 6= 0
Determine the value of the test statistic and the associated
p-value.
Test Statistic =
p-Value =
Correct Answers:
• 0.100345856270442
14. (1 pt)
In a two-tail test for the population mean, the null hypothesis
will be rejected at the α level of significance if the value of the
standardized test statistic z is such that:
• A. −zα < z < zα
• B. z > z−α
• C. z > zα
• D. |z| > zα/2
In a one-tail test for the population mean, if the null hypothesis is not rejected when the alternative hypothesis is true,
• A. a two-tail test should be used instead of a one-tail
test
• B. a Type II error is committed
• C. no error has been made
• D. a Type I error is committed
Correct Answers:
• 8.71757644051023
• 0.00317748
18. (1 pt) Suppose that we are to conduct the following hypothesis test:
H0 : µ = 1070
H1 : µ > 1070
Suppose that you also know that σ = 230, n = 85, x̄ = 1125.2,
and take α = 0.05. Draw the sampling distribution, and use it to
determine each of the following:
A. The value of the standardized test statistic:
Note: For the next part, your answer should use interval notation. An answer of the form (−∞, a) is expressed (-infty, a), an
answer of the form (b, ∞) is expressed (b, infty), and an answer
of the form (−∞, a) ∪ (b, ∞) is expressed (-infty, a)U(b, infty).
B. The rejection region for the standardized test statistic:
Correct Answers:
• D
• B
15. (1 pt)
In a given hypothesis test, the null hypothesis can be rejected
at the 0.10 and the 0.05 level of significance, but cannot be rejected at the 0.01 level. The most accurate statement about the
p−value for this test is:
• A. p-value = 0.01
• B. p-value = 0.10
• C. 0.05 < p-value < 0.10
• D. 0.01 < p-value < 0.05
Which of the following statements is (are) not true?
• A. The probability of making a Type II error increase
as the probability of making a Type I error decreases.
• B. The probability of making a Type II error and the
level of significance are the same.
• C. The power of the test decreases as the level of significance decreases.
• D. All of the above statements are not true
C. The p-value is
D. Your decision for the hypothesis test:
•
•
•
•
A. Do Not Reject H1 .
B. Do Not Reject H0 .
C. Reject H1 .
D. Reject H0 .
Correct Answers:
• 2.21269066975029
• (1.64485,infinity)
• 0.0134595
• D
19. (1 pt) Determine the probability of making a Type II error
for the following hypothesis test, given that µ = 983.
H0 : µ = 970
H1 : µ > 970
For this test, take σ = 46, n = 22, and α = 0.04.
P(Type II Error) =
Correct Answers:
• D
• B
3
Correct Answers:
• 0.664631858013496
c
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