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11. a.
b.
z=
x − 0
/ n
14.15 − 15
=
3/ 50
= −2.00
Because z < 0, p-value is two times the lower tail area
Using normal table with z = -2.00: p-value = 2(.0228) = .0456
c.
p-value .05, reject H0
d.
Reject H0 if z -1.96 or z 1.96
-2.00 -1.96, reject H0
17. a.
b.
H0: = 24.57
Ha: 24.57
z=
x − 0
/ n
=
23.89 − 24.57
2.4 / 30
= −1.55
Because z < 0, p-value is two times the lower tail area
Using normal table with z = -1.55: p-value = 2(.0606) = .1212
c.
p-value > .05, do not reject H0. We cannot conclude that the population mean hourly wage for
manufacturing workers differs significantly from the population mean of $24.57 for the goodsproducing industries.
d.
27. a.
b.
Reject H0 if z -1.96 or z 1.96
z = -1.55; cannot reject H0. The conclusion is the same as in part (c).
H0: 13.04
Ha: < 13.04
t=
x − 0
s/ n
=
12.75 − 13.04
2 / 100
= −1.45
Degrees of freedom = n – 1 = 99
p-value is the lower tail area at the test statistic
Using t table: p-value is between .05 and .10
Exact p-value corresponding to t = -1.45 is .0751
c.
p-value > .05; do not reject H0. We cannot conclude that the cost of a restaurant meal is significantly
cheaper than a comparable meal fixed at home.
d.
df = 99
t.05 = -1.66
Reject H0 if t -1.66
-1.45 > -1.66; do not reject H0
34. a.
b.
H0: = 2
H a: 2
x=
c.
s=
d.
t=
xi 22
=
= 2.2
n
10
( xi − x )
2
n −1
x − 0
s/ n
=
= .516
2.2 − 2
.516 / 10
= 1.22
Degrees of freedom = n - 1 = 9
Because t > 0, p-value is two times the upper tail area
Using t table: area in upper tail is between .10 and .20; therefore, p-value is between .20 and .40.
Exact p-value corresponding to t = 1.22 is .2535
e.
41. a.
b.
p-value > .05; do not reject H0. No reason to change from the 2 hours for cost estimating purposes.
H0: p .53
Ha: p < .53
z=
p − p0
p0 (1 − p0 )
n
=
.46 − .53
.53(1 − .53)
300
= −2.43
p-value is the lower-tail area at the test statistic
Using normal table with z = ˗2.43: p-value =.0075
c.
p-value = .01 ; reject H0. We conclude that there has been a statistically significant decline in
the proportion of American families owning stocks or stock funds over the ten-year period.
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