Question

A sample of 104 observations indicated that
X_{1} is 80. A second sample of 141 observations
indicated that X_{2} is 106. Conduct
a *z*-test of hypothesis about a difference in population
proportions using a 0.01 significance level.

*H*_{0}:
p_{1} - p_{2} = 0

*H*_{1}: p_{1} -
p_{2} ≠ 0

**a)**State the decision
rule.Reject *H*_{0} in favour
of *H*_{1} if the computed value of the
statistic is between -2.58 and
2.58.Reject *H*_{0} in favour
of *H*_{1} if the computed value of the
statistic is less than
2.58.Reject *H*_{0} in favour
of *H*_{1} if the computed value of the
statistic is greater than
2.58.Reject *H*_{0} in favour
of *H*_{1} if the computed value of the
statistic is less than -2.33 or greater than
2.33.Reject *H*_{0} in favour
of *H*_{1} if the computed value of the
statistic is between -2.33 and
2.33.Reject *H*_{0} in favour
of *H*_{1} if the computed value of the
statistic is less than -2.58 or greater than 2.58.None of the
above.

**b)** Compute the pooled proportion.

For full marks your answer should be accurate to at least four
decimal places.

Pooled proportion:

**c)** What is the value of the test
statistic?

For full marks your answer should be accurate to at least three
decimal places.

Test statistic:

**d)**What is your decision
regarding *H*_{0}?There is sufficient evidence,
at the given significance level, to
reject *H*_{0}, and
accept *H*_{1} or at least there is not
enough evidence to reject *H*_{1}.There is
insufficient evidence, at the given significance level, to
reject *H*_{0}.There is insufficient evidence to
reject or not reject the null hypothesis.

Answer #1

A sample of 90 observations indicated that X1 is 62.
A second sample of 146 observations indicated that X2 is
93. Conduct a z-test of hypothesis about a difference in
population proportions using a 0.04 significance level.
H0: p1 -
p2 ≥ 0
H1: p1 - p2
< 0
a)
State the decision rule.
Reject H0 in
favour of H1 if the computed value of the
statistic is less than -2.05 or greater than 2.05.
Reject H0 in
favour of...

A sample of 5 observations from the population indicated that
sample variance s12 is 441. A second sample of 10 observations from
the same population indicated that sample variance s22 is 196.
Conduct the following test of hypothesis using a 0.05 significance
level. H0: σ12 = σ22 H1: σ12 < σ22 You should use the tables in
the book for obtaining the F values. For full marks your answer
should be accurate to at least two decimal places. a) State...

A sample of 8 observations from the population indicated that
sample variance s12 is 784. A second sample
of 8 observations from the same population indicated that sample
variance s22 is 144. Conduct the following
test of hypothesis using a 0.05 significance level.
H0: σ12 =
σ22
H1: σ12 <
σ22
You should use the tables in the book for obtaining the
F values.
For full marks your answer should be accurate to at least two
decimal places.
a)
State...

A sample of scores for men and women from an examination in
Statistics 201 were:
Men
82
74
93
88
75
52
93
48
91
56
51
Women
82
79
82
55
89
75
60
63
72
47
Given that the null hypothesis and the alternative hypothesis
are:
H0: μm -
μw ≤ 5
H1: μm - μw
> 5
and using a 0.05 significance level conduct a t-test
about a difference in population means:
a)
What is the correct...

A sample of scores for men and women from an examination in
Statistics 201 were:
Men
62
91
92
77
69
86
64
60
94
Women
51
79
62
88
80
50
87
65
Given that the null hypothesis and the alternative hypothesis
are:
H0: μm -
μw = -5
H1: μm - μw ≠
-5
and using a 0.05 significance level conduct a t-test
about a difference in population means:
a)
What is the correct decision rule?
Reject H0...

A sample of scores for men and women from an examination in
Statistics 201 were:
Men
68
88
57
56
74
76
95
Women
55
76
70
81
58
56
87
86
46
47
Given that the null hypothesis and the alternative hypothesis
are:
H0: μm -
μw ≤ -1
H1: μm - μw
> -1
and using a 0.025 significance level conduct a t-test
about a difference in population means:
a)
What is the correct decision rule?
Reject H0...

A sample of scores for men and women from an examination in
Statistics 201 were:
Men
78
69
45
81
72
82
84
46
58
Women
67
49
88
59
80
73
91
61
45
Given that the null hypothesis and the alternative hypothesis
are:
H0: μm -
μw ≤ 3
H1: μm - μw
> 3
and using a 0.025 significance level conduct a t-test
about a difference in population means:
a)
What is the correct decision rule?
Reject...

A sample of scores for men and women from an examination in
Statistics 201 were:
Men
88
70
87
53
45
58
71
48
61
81
Women
70
77
60
84
74
89
94
50
66
61
Given that the null hypothesis and the alternative hypothesis
are:
H0: μm -
μw ≤ -2
H1: μm - μw
> -2
and using a 0.05 significance level conduct a t-test
about a difference in population means:
a)
What is the correct decision...

A sample of scores for men and women from an examination in
Statistics 201 were:
boys
72
50
50
93
90
47
80
58
girls
74
98
45
70
67
56
64
91
72
Given that the null hypothesis and the alternative hypothesis
are:
H0: μm -
μw ≤ -1
H1: μm - μw
> -1
and using a 0.025 significance level conduct a t-test
about a difference in population means:
a)
What is the correct decision rule?
Reject H0...

The Longley family owns a large grape vineyard in the Niagara
Peninsula. The grapevines must be sprayed at the beginning of the
growing season to protect against various insects and diseases. Two
new insecticides have just been marketed: Datif and Censor. To test
their effectiveness, 8 long rows were selected. 4 rows were sprayed
with Datif and 4 were sprayed with Censor. When the grapes ripened,
350 of the vines treated with Datif were checked for infestation.
Likewise, a sample...

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