Question

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 is the value of β, i.e., probability of Type II error when true µ = 3?

A. 0.087 B. 0.100 C. 0.050 D. 0.953

3. An appropriate p-value for testing H0 : µ = 0 vs. Ha : µ = 0 with a test statistic (following normal 6 distribution) value z0 = 2.33 should be

A. 0.05 B. 0.02 C. 0.01 D. 0.90

4. A 95% confidence interval (C.I.) for µ is (2.5, 3.9), which means

A. we are 95% confident that the sample mean X¯ lies between (2.5, 3.9).

B. we are 95% confident that the population mean µ lies between (2.5, 3.9).

C. the probability that the sample mean X¯ lies between (2.5, 3.9) is 0.95.

D. the probability that the population mean µ lies between (2.5, 3.9) is 0.95.

Answer #1

To test H0: µ = 42.0 vs.
HA: µ ≠ 42.0, a sample of
n = 40
will be taken from a large population with σ=
9.90.
H0 will be rejected if the sample
mean is less than 40.3 or greater than
43.7.
Find and state the level of significance, α, to
three (3) places of decimal.

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...

7. Suppose you are testing H0 : µ = 10 vs H1 : µ 6= 10. The
sample is small (n = 5) and the data come from a normal population.
The variance, σ 2 , is unknown. (a) Find the critical value(s)
corresponding to α = 0.10. (b) You find that t = −1.78. Based on
your critical value, what decision do you make regarding the null
hypothesis (i.e. do you Reject H0 or Do Not Reject H0)?

Suppose that the following hypothesis were tested H0:
p = .75 vs HA: p >.75. The resulting p-value was
0.95. Which of the following is most likely the 95% confidence
interval using the same data?
Answers:
(0.55, 0.65)
(0.75, 0.85)
(0.80, 0.90)
(0.85, 0.95)
Question 5
Suppose that the following hypothesis were tested H0:
p = .75 vs HA: p >.75. The resulting p-value was
.005. Which of the following is most likely the 95% confidence
interval using the same...

Suppose that you are testing the hypotheses H0?: p=0.17 vs. HA?:
p?0.17. A sample of size 200 results in a sample proportion of
0.22.
?a) Construct a 99?% confidence interval for p.
?b) Based on the confidence? interval, can you reject H0 at
?=0.01?? Explain. ?
c) What is the difference between the standard error and
standard deviation of the sample? proportion?
?d) Which is used in computing the confidence? interval?

1.For testing H0 : p = 0.5 vs. Ha : p < 0.5 at level α, let a
sample of size n = 100 is taken. What would be an appropriate
rejection region?
A. t0 < tα B. z0 < zα C. z0 > zα D. |z0| > zα/2
2. A test statistic
A. is a function of a random sample used to test a hypothesis.
B. is a function of a parameter used to test a hypothesis. C. is...

H0 : µ = 1m
Ha : µ < 1m
test statistic = 2.5
1. what is the sampling distribution for this test
statistic?
2. Level of significance is 0.05, what is the rejection
region?
3. Is this statistically significant? Why/why not?
(i) what does this say about the hypotheses?
4. Would the answer to 3. be different if the level of
significance was 0.01? why?

You are testing H0: µ1 - µ 2 = 0 vs H1: µ1 - µ2 ≠ 0. In doing
so, you are choosing n1 observations from population 1, and n2
observations from population 2. Keeping the same total N = 100 = n1
+ n2, compute the power of the test to detect a difference of 0.6,
with a population standard deviation of 1.0 when: n1 = 0.1×n2, n1 =
0.2×n2, n1 = 0.3×n2, …, n1 = 1.0×n2, n1 =...

Consider the following hypothesis test: H0: µ = 15 Ha: µ ≠ 15 A
sample of 50 provided a sample mean of 14.15. The population
standard deviation is 3. A.) Compute the value of the test
statistic. (Round to two decimal places). B.) What is the p-value?
(Round to three decimal places) C.) Using a=0.01, what is your
conclusion? D.) Using the critical value approach for the 99%
confidence level, what is the critical value? what is the rejection
rule?...

Consider the following hypothesis test
H0 : µ ? 12
Ha : µ > 12
A sample of 25 provided a sample mean x= 14 and a sample
standard deviation s = 4.32
a. what is the value of the test statistic?
b. At ? = 0.05, what is your conclusion ?

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