Question

Consider a multinomial experiment with n = 275 and k = 4. The null hypothesis to be tested is H0: p1 = p2 = p3 = p4 = 0.25. The observed frequencies resulting from the experiment are: (You may find it useful to reference the appropriate table: chi-square table or F table)

Category 1 2 3
4

Frequency 67 55 75
78

a. Choose the appropriate alternative hypothesis.

Not all population proportions are equal to 0.25.

All population proportions differ from 0.25.

b-1. Calculate the value of the test statistic. (Round
intermediate calculations to at least 4 decimal places and final
answer to 3 decimal places.)

b-2. Find the p-value.

0.025 p-value < 0.05

p-value < 0.01

p-value 0.10

0.01 p-value < 0.025

0.05 p-value < 0.10

c. At the 10% significance level, what is the conclusion to the
hypothesis test?

Reject H0 since the p-value is greater than the significance
level.

Reject H0 since the p-value is less than the significance
level.

Do not reject H0 since the p-value is greater than the significance
level.

Do not reject H0 since the p-value is less than the significance
level.

Answer #1

Consider a multinomial experiment with n = 307 and
k = 4. The null hypothesis to be tested is
H0: p1 =
p2 = p3 =
p4 = 0.25. The observed frequencies resulting
from the experiment are: (You may find it useful to
reference the appropriate table: chi-square tableor F
table)
Category
1
2
3
4
Frequency
85
58
89
75
b-1. Calculate the value of the test statistic.
(Round intermediate calculations to at least 4 decimal
places and final...

A multinomial experiment produced the following results: (You
may find it useful to reference the appropriate table: chi-square
table or F table) Category 1 2 3 4 5
Frequency 57 63 70 55 55
a. Choose the appropriate alternative hypothesis to test if the
population proportions differ. All population proportions differ
from 0.20. Not all population proportions are equal to 0.20.
b. Calculate the value of the test statistic. (Round
intermediate calculations to at least 4 decimal places and final...

Consider a multinomial
experiment with n = 350 and k = 3. The null
hypothesis is H0: p1 =
0.60, p2 = 0.30, and p3 =
0.10. The observed frequencies resulting from the experiment are:
(You may find it useful to reference the appropriate table:
chi-square table or F table)
Category
1
2
3
Frequency
216
100
34
a.
Choose the appropriate alternative hypothesis.
All population proportions differ from their hypothesized
values.
At least one of the population proportions differs...

n order to conduct a hypothesis test for the population
proportion, you sample 290 observations that result in 87
successes. (You may find it useful to reference the appropriate
table: z table or t table) H0: p ≥ 0.35; HA: p < 0.35.
a-1. Calculate the value of the test statistic. (Negative value
should be indicated by a minus sign. Round intermediate
calculations to at least 4 decimal places and final answer to 2
decimal places.)
a-2. Find the p-value....

In order to conduct a hypothesis test for the population mean, a
random sample of 24 observations is drawn from a normally
distributed population. The resulting sample mean and sample
standard deviation are calculated as 13.9 and 1.6, respectively.
(You may find it useful to reference the appropriate
table: z table or t
table).
H0: μ ≤ 13.0 against
HA: μ > 13.0
a-1. Calculate the value of the test statistic.
(Round all intermediate calculations to at least 4 decimal...

In order to conduct a hypothesis test for the population mean, a
random sample of 28 observations is drawn from a normally
distributed population. The resulting sample mean and sample
standard deviation are calculated as 17.9 and 1.5, respectively.
(You may find it useful to reference the appropriate
table: z table or t
table).
H0: μ ≤ 17.5 against
HA: μ > 17.5
a-1. Calculate the value of the test statistic.
(Round all intermediate calculations to at least 4 decimal...

A multinomial experiment produced the following results:
Category
1
2
3
Frequency
139
120
71
a.
Choose the appropriate alternative hypothesis at
H0: p1 = 0.40,
p2 = 0.40, and p3 =
0.20.
All population proportions differ from their hypothesized
values.
At least one of the population proportions differs from its
hypothesized value.
b.
Calculate the value of the test statistic at
H0: p1 = 0.40,
p2 = 0.40, and p3 = 0.20....

In order to conduct a hypothesis test for the population mean, a
random sample of 20 observations is drawn from a normally
distributed population. The resulting sample mean and sample
standard deviation are calculated as 10.5 and 2.2, respectively.
(You may find it useful to reference the appropriate table: z table
or t table).
H0: μ ≤ 9.6 against HA: μ > 9.6
a-1. Calculate the value of the test statistic. (Round all
intermediate calculations to at least 4 decimal...

Consider the following competing hypotheses and accompanying
sample data. (You may find it useful to reference the
appropriate table: z table or t
table)
H0: p1 −
p2 ≥ 0
HA: p1 −
p2 < 0
x1 = 250
x2 = 275
n1 = 400
n2 = 400
a. Calculate the value of the test statistic.
(Negative value should be indicated by a minus sign. Round
intermediate calculations to at least 4 decimal places and final
answer to 2 decimal...

In order to conduct a hypothesis test for the population mean, a
random sample of 24 observations is drawn from a normally
distributed population. The resulting sample mean and sample
standard deviation are calculated as 4.8 and 0.8, respectively.
(You may find it useful to reference the appropriate
table: z table or t
table)
H0: μ ≤ 4.5 against
HA: μ > 4.5
a-1. Calculate the value of the
test statistic. (Round all intermediate calculations to at
least 4 decimal...

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