Question

Perform a hypothesis test for the mean for the following sample. The significance level alpha is 5%.

Sample: 7.9, 8.3, 8.4, 9.6, 7.7, 8.1, 6.8, 7.5, 8.6, 8, 7.8, 7.4, 8.4, 8.9, 8.5, 9.4, 6.9, 7.7.

Test if mean≠8.7.

Assume normality of the data.

1 Formulate the hypothesis by entering the corresponding signs:
"<", ">", "=" or "≠" and numbers. **Hint: in your
answers use "<>" instead of "≠".**

H0: mean

H1:mean

2 p-value (rounded to three decimal places):

3 Conclusions, based on the results, which of the following options is correct: (type the corresponding capital letter, do not type the "dot" at the end)

- Reject H0 and accept H1 at 5% significance level.
- Accept H0 with 95% confidence.
- Do not reject H0 at 5% significance level and reserve judgement. We may retain H0 but with some unknown probability.
- Reject both, H0 and H1, the test has failed.
- Accept both, H0 and H1, the test has failed.

Answer #1

You perform a hypothesis test for a hypothesized population mean
at the 0.01 level of significance. Your null hypothesis for the
two-sided test is that the true population mean is equal to your
hypothesized mean. The two-sided p-value for that test is 0.023.
Based on that p-value... A. you should accept the null hypothesis.
B. the null hypothesis cannot be correct. C. you should reject the
null hypothesis. D. you should fail to reject the null
hypothesis.

Given contingency table for simultaneous occurance of two
categorical random variables X (levels A,B,C) and Y (levels
L1,L2,L3)
L1
L2
L3
A
20
40
20
B
40
30
15
C
45
50
30
Determine the marginal probability P ( Y = L 1 )
= (round to the third decimal place)
Determine the conditional probability P ( X = A | Y = L 1 )
= (round to the second decimal place)
Use R to conduct a chi-square test of independence...

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...

A researcher did a one-tailed hypothesis test using an alpha
level of .01, H0 was rejected.A colleague analyzed the same data
but used a two-tailed test with α=.05, H0 was failed to reject. Can
both analyses be correct? Explain your answer.

On your first day on the job, your boss asks you to conduct a
hypothesis test about the mean dwell time of a new type of UAV.
Before you arrived, an experiment was conducted on n= 5 UAVs (all
of the new type) resulting in a sample mean dwell time of y-bar=
9.4 ℎours. The goal is to conclusively demonstrate, if possible,
that the data supports the manufacturer’s claim that the mean dwell
time is greater than 10 hours. Given...

For each situation, perform a hypothesis test for the population
mean. Be sure to show the null hypothesis H0 (with correct
parameter), the alternative hypothesis H1, the P-level you get from
ZTest, TTest, or 1-PropZTest (depending on whether you’re testing
for µ or p, and whether
σ is known or unknown), the result of the test
(i.e. reject / do not reject H0) and the conclusion (interpret the
result in English).
Studies suggest that 10% of the world’s population is...

A sample of 42 observations is selected from a normal
population. The sample mean is 28, and the population standard
deviation is 8.
Conduct the following test of hypothesis using the 0.05
significance level.
H0 : μ ≤ 27
H1 : μ > 27
a. Is this a one- or two-tailed test?
b. What is the decision rule? (Round
the final answer to 3 decimal places.)
(Reject or
Accept) H0
and (accept or
reject) H1 when
z >___ .
c. What is the...

A recent national survey found that high school students watched
an average (mean) of 7.7 movies per month with a population
standard deviation of 0.9. The distribution of number of movies
watched per month follows the normal distribution. A random sample
of 46 college students revealed that the mean number of movies
watched last month was 7.0. At the 0.05 significance level, can we
conclude that college students watch fewer movies a month than high
school students?
1.State the null...

A sample of 60 observations is selected from a normal
population. The sample mean is 37, and the population standard
deviation is 8.
Conduct the following test of hypothesis using the 0.10
significance level.
H0 : μ ≤ 36
H1 : μ > 36
a. Is this a one- or two-tailed test?
One-tailed test or Two-tailed test
b. What is the decision rule? (Round
the final answer to 3 decimal places.)
(Reject or Accept) H0
and (accept or reject H1
when z >...

Test whether μ1<μ2 at the alpha α equals =0.01 level of
significance for the sample data shown in the accompanying table.
Assume that the populations are normally distributed.
Population 1
Population 2
n
33
25
x̅
103.4
114.2
s
12.3
13.3
Determine the null and alternative hypothesis for this test.
B.
H0:μ1=μ2
H1:μ1<μ2
Determine the P-value for this hypothesis test.
P=__?__
(Round to three decimal places as needed.)

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