Key for STAT 250 Exam #2
Exam A
1. One sample Z-test
(a) H0 : µ ≤ 4.91, HA : µ > 4.91
(b) z∗ = 5.6−4.91
= 2.17
1.03
√
80
(c) p-value = P (Z > 2.17) = 0.015. Reject H0
(d) There is enough evidence to suggest that the average weight of king crab has
increased since 2010.
2. Condence interval for a proportion
(a) p̂ =
16
210
= .076
q
(b) .076 ± 1.96
.076(1−.076)
210
=(4.0%,11.1%). If you used R: (4.6%,12.2%)
3. Z-table
(a)
(b)
(c)
(d)
P (X > 61)=33.3%. 1-pnorm(61,58,7)
P (x̄ > 61) =0.3%. 1-pnorm(61,58,7/sqrt(40))
P (x̄ < 57) =15.6%. pnorm(57,58,7/sqrt(50))
P (56 < x̄ < 60) = P (x̄ < 60)−P (x̄ < 56)=93.0% pnorm(60,58,7/sqrt(40))-pnorm(56,58,7/
4. Error question
(a) Type I: Conclude that 5-hour energy drink reduces the lifespan of a zebra sh,
when the lifespan in fact it stays the same or increases.
(b) Type II: Conclude that 5-hour energy drink does not reduces the lifespan of a
zebra sh, when in fact it does reduce the lifespan of a zebra sh.
5. Condence interval for a mean sample size
(a) n =
2.576(.72) 2
.3
= 38.2 = 39 samples
6. Condence interval for a mean
(a) 76 ± 1.645
√9
35
=(75.5,78.5) cm. Technically, there should be no decimal places.
7. Sample size for proportion (either is correct)
(a) .6(.4)
1.96
.04
2
= 577 samples
1
(b) .5(.5)
1.96
.04
2
= 601 samples
8. One sample Z-test
(a) H0 : µ ≥ 2.45, HA : µ < 2.45
(b) z∗ = 2.37−2.45
= −1.39
.34
√
35
(c) p-value = P (Z < −1.39) = 0.082. Fail to Reject H0
(d) There is not enough evidence to suggest that the average height of corn is reduced
by drought.
9. Retrieving information from Condence Interval
= 2.9g
(a) Mean: 2.65+31.5
2
s
(b) SD: 1.96 √49 = .25 ⇒ s = .90g
2
Exam B
1. One sample Z-test
(a) H0 : µ ≥ 2.56, HA : µ < 2.56
(b) z∗ = 2.48−2.56
= −2.05
.29
√
55
(c) p-value = P (Z < −2.05) = 0.02. Reject H0
(d) There is enough evidence to suggest that the average height of corn is reduced by
drought.
2. Condence interval for a mean
(a) 76 ± 1.96
√9
35
=(73.0,79.0)cm. Technically, there should be no decimal places.
3. Z-table
(a)
(b)
(c)
(d)
P (X > 59)=37.1%. 1-pnorm(59,57,6)
P (x̄ > 59) =0.9%. 1-pnorm(59,57,6/sqrt(50))
P (x̄ < 56) =14.7%. pnorm(56,57,7/sqrt(40))
P (55 < x̄ < 60) = P (x̄ < 60)−P (x̄ < 55)=96.3% pnorm(60,57,6/sqrt(30))-pnorm(55,57,6/
4. Error question
(a) Type I: Conclude that 5-hour energy drink reduces the lifespan of a zebra sh,
when the lifespan in fact it stays the same or increases.
(b) Type II: Conclude that 5-hour energy drink does not reduces the lifespan of a
zebra sh, when in fact it does reduce the lifespan of a zebra sh.
5. Condence interval for a mean sample size
(a) n =
1.645(.61) 2
.15
= 44.7 = 45 samples
6. Condence interval for a proportion
(a) p̂ =
22
250
= .088
q
(b) .088 ± 2.576
.088(1−.088)
250
=(4.2%,13.4%). If you used R: (5.0%,14.8%)
7. Sample size for proportion (either is correct)
(a) .8(.2)
(b) .5(.5)
1.96
.03
1.96
.03
2
= 683 samples
2
= 1068 samples
8. One sample Z-test
3
(a) H0 : µ ≤ 4.85, HA : µ > 4.85
(b) z∗ = 5.05−4.85
= 1.22
1.27
√
60
(c) p-value = P (Z > 1.22) = 0.111. Fail to Reject H0
(d) There is not enough evidence to suggest that the average weight of king crab has
increased since 2010.
9. Retrieving information from Condence Interval
= 2.9g
(a) Mean: 2.65+31.5
2
(b) SD: 1.96 √s49 = .25 ⇒ s = .90g
4