Question

**Describe with details**

Testing hypotheses about a population mean µ when a large (? > 30) random sample is available.

Problem I: The state department of education in a particular state claims that the mean height of a first grader is 42 inches. A researcher in a particular region of the state believes the mean height of first grade students in this region exceeds 42 inches. The researcher will examine height data for 73 first graders in the region and can tolerate the size of the Type I error being α = 0.05. A. Do this steps written description for this hypothesis test. The test to use here is a 1-sample z-test with 72 degrees of freedom.

1. A description the null and alternative hypotheses in terms of the problem.

2. A statement of the null and alternative hypotheses in standard symbols.

3. The significance level (size of the Type I error), α, that will be tolerated.

4. The name of the statistical test to be used and the assumptions required in order for the test to be valid.

5. A clear description of exactly what the decision rule is; i.e. under what circumstances is the null hypothesis rejected.

Answer #1

A researcher wants to support the claim that students
spend less than 7 hours per week doing homework. The sample size
for the test is 64 students. The drawing shown diagrams a
hypothesis test for population mean under the Null Hypothesis (top
drawing) and under the Alternative Hypothesis (bottom
drawing).
State the Null and Alternative Hypotheses.
What is the design probability associated with Type I
error?
What is the design probability associated with Type II
error?
What is the power...

A normal population has mean "µ" and standard deviation 12. The
hypotheses to be tested are H0: µ = 40 versus H1: µ > 40.
Which would result in the highest probability of a Type II
error?
µ = 42; n = 100
µ = 42; n = 10
µ = 41; n = 100
µ = 41; n = 10
µ = 40.9; n = 15
If a random sample has 100 observations, the true population
mean is 42,...

steel factory produces iron rods that are supposed to
be 36 inches long. The machine that makes
these rods does not produce each rod exactly 36 inches long. The
lengths of these rods vary slightly.
It is known that when the machine is working properly, the mean
length of the rods is 36 inches.
According to design, the standard deviation of the lengths of all
rods produced on this machine is
always equal to .05 inches. The quality control department...

Questions 21-28: Does consuming sports energy drinks
improve endurance? For the general population, scores on an
endurance task have a mean of 50 with a standard deviation of 12. A
sample of 50 students is given energy drinks and their mean
performance on the endurance task is 53. Use an alpha level of
0.01
21. Using symbols state the null hypothesis
22. Using symbols state the alternative hypothesis
23. Is this a one-tailed or two tailed test?
24. Where would...

Mean: 0.273 Median: 0.266. Sample Size: 30
Standard Deviation: 0.019 IQR: 0.022
Hypothesis is: µ= 0.256 µ>
0.256
α=0.05
-State the conclusion to the hypothesis test, including
the p-value for the test and a proper conclusion (reject the null
hypothesis or fail to reject the null hypothesis) and what we then
conclude about the population mean.
Report the confidence interval you
calculated.
i.
Make sure you state it is a confidence interval for
mean.
ii.
Give the proper interpretation of the...

A random
sample is selected from a normal population with a mean of µ = 30
and a standard deviation of σ= 8. After a treatment is administered
to the individuals in the sample, the sample mean is found to be x̅
=33.
Furthermore,
if the sample consists of n = 64 scores, is the sample
mean sufficient to conclude that the treatment has a significant
effect? Use a two-tailed test with α = .05.
4a. Which of
the following...

It is known that the status quo of the population mean is 88. A
sample of size 50 is taken and the sample mean is computed as 85.
You decided to reject the null hypothesis that the population mean
is at least 88 and to be in favor of the alternative hypothesis
that the population mean is less than 88.
Select one:
A. We may commit a Type II error if the null hypothesis
is false.
B. We may commit...

A researcher suspects that the mean pollutant level in a region
is higher than the state average of 4.3 grams/cubic
liter. Data are collected; from 56 samples, the mean is
found to be 5.4, with a standard deviation of 5.0. Test
the null hypothesis that the true mean in the region is 4.3,
against the alternative that it is higher. State the
null and alternative hypotheses, give the critical value, find the
test statistic, make a decision, and give the p-value.

A researcher suspects that the mean pollutant level in a region
is higher than the state average of 4.3 grams/cubic liter. Data are
collected; from 56 samples, the mean is found to be 5.4, with a
standard deviation of 5.0. Test the null hypothesis that the true
mean in the region is 4.3, against the alternative that it is
higher. State the null and alternative hypotheses, give the
critical value, find the test statistic, make a decision, and give
the...

A researcher suspects that the mean pollutant level in a region
is higher than the state average of 4.3 grams/cubic liter. Data are
collected; from 56 samples, the mean is found to be 5.4, with a
standard deviation of 5.0. Test the null hypothesis that the true
mean in the region is 4.3, against the alternative that it is
higher. State the null and alternative hypotheses, give the
critical value, find the test statistic, make a decision, and give
the...

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