stat analysis homework and excel lab
farhm9
ic07.docCalifornia State University, Fresno Name:
DS 123 MW, Fall 2016, IC 07
Problem 1. For each of the following null hypotheses and given levels,
(i) State the alternative hypothesis.
(ii) Label the value of the critical bound(s) in z on the bottom axis.
(iii) Draw, label, and shade the appropriate rejection region.
(iv) State the decision rule.
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a. 13 . 0 : 0 ³ p H : A H = 0.10 Decision Rule:
|
|
b. 90 . 0 : 0 £ p H : A H = 0.025 Decision Rule:
|
|
c. . 267 . 0 : 0 = p H : A H = 0.02 Decision Rule:
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Problem 2. A manufacturer of drip irrigation controllers is interested in reporting an interval estimate for the proportion of manufactured units that are defective. A random sample of 500 controllers determined that 10 were defective.
a. What is the point estimate for the proportion of 2a. manufactured units that are defective?
b. Between what two bounds can we be 95% confident that the interval estimate contains the true defective rate of all drip irrigation controllers?
2b. Lower bound:
2b. Upper bound:
Problem 3. The policy of a regional transit authority is to add a bus route if more than 55 percent of the potential commuters indicate they would use the particular route. A sample of 70 commuters revealed that 49 would use a proposed route into the downtown area. Using the 0.05 level of significance, determine whether the proposed route satisfies the transit authority’s criterion.
3. State the appropriate values from the problem.
a. Population proportion, p = b. Sample proportion
=
p
ˆ
c. Sample size,
=
n
4. What are the best hypotheses to use to test whether the new route meets the criterion established by the regional transit authority?
(a)
55
.
0
:
55
.
0
:
0
¹
=
p
H
p
H
A
(b)70
.
0
:
70
.
0
:
0
¹
=
p
H
p
H
A
(c)55
.
0
:
55
.
0
:
0
<
³
p
H
p
H
A
(d)
70
.
0
:
70
.
0
:
0
<
³
p
H
p
H
A
(e)55
.
0
:
55
.
0
:
0
>
£
p
H
p
H
A
(f)70
.
0
:
70
.
0
:
0
>
£
p
H
H
A
5. At a significance level of 0.01, state the best critical value and decision rule to test the hypotheses.
(a) z = 2.326 (b) z = 2.576
Reject H0 if z > 2.326 Reject H0 if z > 2.576
(c) t = 2.382 (d) t = 2.649 Reject H0 if t > 2.382 Reject H0 if t > 2.649
6. Which is the best calculation to use in computing the value of the test statistic?
(a)
70
45
.
0
55
.
0
)
55
.
0
70
.
0
(
×
-
=
z
(b)70
45
.
0
55
.
0
)
70
.
0
55
.
0
(
×
-
=
z
(c)70
30
.
0
70
.
0
)
70
.
0
55
.
0
(
×
-
=
z
(d)
70
45
.
0
55
.
0
)
55
.
0
70
.
0
(
×
-
=
t
(e)70
30
.
0
70
.
0
)
70
.
0
55
.
0
(
×
-
=
t
7. If the value of the test statistic is 2.52, what implications should be drawn?
(a) There is enough evidence to conclude the proposed route satisfies the transit authority’s criterion.
(b) There is enough evidence to conclude the proposed route does not satisfy the transit authority’s criterion.
(c) There is not enough evidence to conclude the proposed route satisfies the transit authority’s criterion.
(d) There is not enough evidence to conclude the proposed route does not satisfy the transit authority’s criterion.
8. True False The transit authority should not add the new bus route.
