Question

We are testing the hypothesis

H0:p=.75

Ha:p<.75

for the # the proportion of people who find an enrollment
website “easy to use.” The test will be based on a simple random
sample of size 400 and at a 1% level of significance. Recall that
the sample proportion vary with mean p and standard deviation

= sqroot( p(1-p)/n)

You shall reject the null hypothesis if

The P_value of the test is less than 0.01

a) Find the probability of a type II error if in fact

p=0.72

b) Find the probability of a type II error if in fact

p=0.65

c) Find the probability of a type II error if in fact

p=0.60

Answer #1

a)

( please try 0.8186 if this comes wrong)

b)

( please try 0.0188 if this comes wrong)

c)

Suppose we wish to test H0:p≤0.3H0:p≤0.3 vs
HA:p>0.3HA:p>0.3 where pp is a binomial parameter. If XX
represents the number of successes in 8080 trials, and the null
hypothesis is rejected whenever X≥30X≥30, calculate:
a) αα, the probability of type I error.
b) ββ, the probability of type II error when pp = 0.380.38, and
the power of the test.

We are conducting a test of the hypotheses
(H0:p=0.8)
versus
(Ha:p≠0.8)
.
We find a p-value of 0.0062. What conclusion can be made about
these hypotheses?
Select one or more:
a. We should NOT reject the null hypothesis.
b. There is not enough evidence to suggest that the proportion
is not 0.8.
c. We should reject the null hypothesis.
d. There is enough evidence to suggest that the proportion is
0.8.
e. There is evidence to suggest that the proportion...

1. In testing a null hypothesis H0 versus an alternative Ha, H0
is ALWAYS rejected if
A. at least one sample observation falls in the non-rejection
region.
B. the test statistic value is less than the critical value.
C. p-value ≥ α where α is the level of significance. 1
D. p-value < α where α is the level of significance.
2. In testing a null hypothesis H0 : µ = 0 vs H0 : µ > 0,
suppose Z...

In a test of H0: p=.61] against
HA:p<.61 , the sample proportion was
found to be p=.593 . Which of the following is a
correct description of the p-value? Please show work and explain
answer, I am reviewing for a final.
the chance of obtaining a sample proportion of .61 or less
the chance of obtaining a sample proportion of .593 or
less
the chance of obtaining a sample proportion greater than
.61
the chance of obtaining a sample proportion...

We are conducting a test of the hypotheses
(H0:p=0.4)
versus
(Ha:p≠0.4)
For our test, we calculate a sample proportion of 0.28 with a
sample size of 50. What is the corresponding p-value? Give your
answer to four decimal places.

. Consider the following hypothesis test: H0 : µ ≥ 20 H1 : µ
< 20 A sample of 40 observations has a sample mean of 19.4. The
population standard deviation is known to equal 2. (a) Test this
hypothesis using the critical value approach, with significance
level α = 0.01. (b) Suppose we repeat the test with a new
significance level α ∗ > 0.01. For each of the following
quantities, comment on whether it will change, and if...

A hypothesis test will be performed to test the claim that a
population proportion is less than 0.70. A sample size of 400 and
significance level of 0.025 will be used. If p = 0.62, find the
probability of making a type II error, β.
Fill in the blanks below to
describe the sampling distribution of ??� assuming H0 is
true.
Mean =
Standard deviation =
Shape:
Sketch the sampling distribution
of ??�assuming H0 is true.
Specify the rejection region...

Consider the following hypothesis test:
H0: p .8
Ha: p > .8
A sample of 500 provided a sample proportion of .853.
i. Determine the standard error of the proportion.
ii. Compute the value of the test statistic.
iii. Determine the p-value; and at a 5% level, test the
above hypotheses.

A hypothesis test will be performed to test the claim that a
population proportion is less than 0.70. A sample size of 400 and
significance level of 0.025 will be used. If p = 0.62, find the
probability of making a type II error, β.
Answer:
A. Fill in the
blanks below to describe the sampling distribution of ??� assuming
H0 is true.
Mean:
Standard
deviation:
Shape:
Sketch the sampling distribution of ??� assuming H0 is
true.
B. Specify...

1. For testing H0 : µ = 0 vs. Ha : µ > 0, H0 is rejected if X
>¯ 1.645, given n = 36 and σ = 6. What is the value of α, i.e.,
maximum probability of Type I error?
A. 0.90 B. 0.10 C. 0.05 D. 0.01
2. For testing H0 : µ = 0 vs. Ha : µ > 0, H0 is rejected if X
>¯ 1.645, given n = 36 and σ = 6. What...

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