STAT 211 – 200
EXAM 4 – FORM A
SUMMER03
Fusible interlinings are being used with increasing frequency to support outer fabrics and improve the
shape and drape of various pieces of clothing. The data on extensibility (%) at 100 gm/cm for both highquality fabric (H) and poor-quality fabric (P) specimens are as follows. Both groups exhibit normally
distributed data.
H
1.2 0.9 0.7 1.0 1.7 1.7 1.1 0.9 1.7 1.9 1.3 2.1 1.6 1.8 1.4 1.3
1.9 1.6 0.8 2.0 1.7 1.6 2.3 2.0
P
1.6 1.5 1.1 2.1 1.5 1.3 1.0 2.6
The following is the descriptive statistics obtained by using MINITAB software.
Variable
H:
P:
N
24
8
Variable
H:
P:
Minimum
0.7000
1.000
Mean
1.5083
1.587
Maximum
2.3000
2.600
Median
1.6000
1.500
TrMean
1.5091
1.587
Q1
1.1250
1.150
StDev
0.4442
0.530
SE Mean
0.0907
0.187
Q3
1.8750
1.975
Answer the following 8 questions using this information.
1.
Which of the following is the point estimate of the true average extensibility for high-quality fabric?
(a) 1.5083
(b) 1.5280
(c) 1.5477
(d) 1.5870
2.
I believe that true average extensibility for high-quality fabric is 1.7. Which of the following
alternative hypothesis that you would use to see if the data support this belief? (Hint:  is the true
average extensibility for high-quality fabric and do not forget we follow the given wording to
formulate them)
(a)   1.7
  1 .7
(c)   1.7
(d)   1.7
(b)
3.
I believe that true average extensibility for high-quality fabric is 1.7. Which of the following is the
corresponding test statistics of testing this belief?
(a) -2.1142
(b) -0.4316
(c) -0.1917
(d) 0.1917
(e) 0.4316
4.
95% confidence interval of the true average extensibility for high-quality fabric is (1.3207 , 1.6959).
Do the data support the claim of true extensibility for high-quality fabric being 1.7 using =0.05?
(a) Yes
(b) No
5.
Which of the following is the point estimate of the true variance of extensibility for high-quality
fabric?
(a) 0.1973
(b) 0.2809
(c) 0.4442
(d) 0.5300
(e) 0.6665
STAT 211 – 200
EXAM 4 – FORM A
SUMMER03
6.
Which of the following is the 90% confidence interval for the true standard deviation of extensibility
for high-quality fabric?
(a) (0.0003 , 0.7805)
(b) (0.1290 , 0.3467)
(c) (0.3592 , 0.5888)
(d) (0.5390 , 0.8835)
7.
I claim that true variance of extensibility for poor-quality fabric is 0.15. Which of the following is the
test statistics for my claim?
(a) 13.109
(b) 30.255
(c) 43.071
(d) 68.111
(e) 81.267
8.
I claimed that true variance of extensibility for poor-quality fabric is 0.15 and computed the P-value
for the corresponding hypothesis between 0.10 and 0.20. Using =0.05, would you reject H0?
(a) Yes
(b) No
(c) Depends on H0
(d) Depends if we have lower tailed, upper tailed or two-tailed test.
A reporter finds out that 15 out of 100 randomly selected highway bridges have serious structural decay. A
professor wants to determine if that finding is consistent with the highway department’s claim that no more
than 11% of the bridges are in need of emergency structural repairs. Let p be the true proportion of
highway bridges with structural decay.
Answer the following 5 questions using this information.
9.
Which of the following null hypothesis you should use to formulate this? (Hint: Do not forget we
follow the given wording to formulate them)
(a) p = 0.15
(b) p  0.11
(c) p  0.15
(d) p > 0.15
(e) p > 0.11
10. Which of the following is the corresponding test statistics for the highway department’s claim?
(a) –1.28
(b) –1.12
(c) 1.05
(d) 1.12
(e) 1.28
11. Do we have enough evidence based on the data to agree with the claim using =0.05?
(a) Yes
(b) No
12. How many highway bridges I should include in my study to estimate the p within 0.01 with 95%
confidence? (Hint: use the current information for the estimator of p)
(a) 1724
(b) 2499
(c) 4899
(d) 9604
STAT 211 – 200
EXAM 4 – FORM A
SUMMER03
13. I have computed the 95% confidence interval for the true proportion of the bridges that are in need of
emergency structural repairs as (0.08001 , 0.21999). Which of the following does this confidence
interval may imply?
(a) At most 11% of the bridges are in need of emergency structural repairs.
(b) More than 11% of the bridges are in need of emergency structural repairs.
(c) Exactly 11% of the bridges are in need of emergency structural repairs.
(d) At least 11% of the bridges are in need of emergency structural repairs.
A researcher claims that at least 10% of all football helmets have manufacturing flaws that could
potentially cause injury to wearer. A sample of 200 helmets revealed that 16 helmets contained such
defects. (Hint: H 0 : p  0.10 versus H a : p  0.10 where p is the true proportion of all football
helmets with manufacturing flaws and X is the number of helmets with manufacturing flaws) Answer the
following 3 questions using this information.
14. Which of the following is the point estimate for p?
(a) 0.05
(b) 0.08
(c) 0.10
(d) 0.16
(e) 0.20
15. Which of the following is the possible rejection region for this claim?
(a) {x; X 3}
(b) {x; X 17}
(c) {x; X 2 or X18}
16. Which of the following is the test statistics and corresponding decision for this claim using
=0.01?(Hint: Notice that you need to first compute the test statistics and then either using the P-value
or the critical value, you should make a decision)
(a) Since the test statistics is –1.043, H0 should be rejected.
(b) Since the test statistics is –1.043, H0 should not be rejected.
(c) Since the test statistics is –0.943, H0 should be rejected.
(d) Since the test statistics is –0.943, H0 should not be rejected.
(e) Since the test statistics is 1.043, H0 should be rejected.
17. If the test statistics is Z=1.23 for the upper tailed test, which of the following is the corresponding Pvalue?
(a) 0.1093
(b) 0.1151
(c) 0.8840
(d) 0.8907
18. Which of the following is the P(7.790< 2 < 26.119) where 2 is a chi-squared random variable with
the sample size n=15?
(a) 0.025
(b) 0.10
(c) 0.125
(d) 0.875
(e) 0.975
19. Which of the following cannot be an alternative hypothesis where  is the true average?
(a)  < 3
(b)   5
(c)  > 1
(d)   0.7
STAT 211 – 200
EXAM 4 – FORM A
SUMMER03
20. Which of the following is the P(0< t < 2.624) where t is a t-distribution random variable with the
sample size n=15?
(a) 0.01
(b) 0.19
(c) 0.49
(d) 0.51
(e) 0.99
21. If the test statistics is t=-1.227 for the lower tailed test where t is a t-distribution random variable with
the sample size n=10, which of the following is the corresponding P-value?
(a) Less than 0.01
(b) Between 0.01 and 0.025
(c) Between 0.025 and 0.05
(d) Between 0.05 and 0.10
(e) More than 0.10
22. In which of the following cases, large sample conditions for constructing the confidence interval for p
^
are not satisfied? (Let p be the true proportion, n be the sample size and
p be the sample proportion)
^
(a) n=100,
p =0.20
(b) n=200,
p =0.97
(c) n=200,
p =0.90
(d) n=100,
p =0.15
^
^
^
23. If the P-value=0.30 and   0.05 , which of the following would be your decision for the legitimate
hypothesis?
(a) I need to know H 0 or H a to answer this question
(b) Reject H0
(c) Fail to reject H0
24. To compute the P-value when
H a :   27 , which of the following you would do?
(a) I would look at the area above the test statistics on the corresponding table
(b) I would look at the area below the test statistics on the corresponding table
(c) I would look at the area above the absolute value of the test statistics on the corresponding table
and multiply by two.
25 The test statistics for testing the true mean is t=1.91 for the upper tailed test and the table value is
t0.025;14=2.145 where n=15 and =0.025. If the specified claim was under the Ha, which of the possible
error you may have made?
(a) Type I error
(b) Type II error
(c) No error