For a normal population with known variance σ2, answer the
following questions:
d. What is the confidence level for the interval μ ≤ x+ 2.00σ∕ √
n?
e. What is the confidence level for the interval x−1.96σ∕ √ n ≤
μ?
Answer the following questions with clear explanation.
a. Explain intuitively what does population mean and variance
tells you about the distribution of a random variable?
b. Can you think of a reason why do we mostly only care about
mean and variance a random variable since the distribution function
could involve more than the two parameters?
c. Explain why we could use a sample data to draw conclusions
about a population parameter?
d. Is p-value of a hypothesis test a...
(Topic: Confidence Interval Estimation for the Mean of a Normal
Distribution: Population Variance Known)
The number of bolts produced each hour
from a particular machine is normally distributed with a standard
deviation of 7.4. For a random sample of 15 hours, the average
number of bolts produced was 587.3.
Find the upper and lower confidence
limits of a 98% confidence interval for the population mean number
of bolts produced per hour.
Find the answer by hand calculation.
Find the answer...
Question: Consider a normal distribution with
mean m and
variance s2. Assume we know that s2 = 4 and suspect that m 6= 3.
Assume further
that we have independently drawn 100 values from the
distribution and have
obtained a sample mean of 5.
(a) Explain the notion of a sampling
distribution and state the central limit
theorem.
(b) Approximately, what is the sampling
distribution in the above situation?
Assume now that we want to conduct a hypothesis test concerning...
Assume a normal population with known variance σ2, a random
sample (n< 30) is selected. Let x¯,s represent the sample mean
and sample deviation. (1)(2pts) write down the formula: 98%
one-sided confidence interval with upper bound for the
population mean. (2)(6pts) show how to derive the confidence
interval formula in (1).
A random sample n=30 is obtained from a population with unknown
variance. The sample variance s2 = 100 and the sample
mean is computed to be 75. Test the hypothesis at α = 0.05 that the
population mean equals 80 against the alternative that it is less
than 80. The null hypothesis Ho: µ = 80 versus the alternative H1:
Ho: µ < 80.
Calculate the test statistic from your sample mean. Then
calculate the p-value for this test using...
Suppose we take a random sample X1,…,X6 from a normal population
with a known variance σ21=4 and unknown mean μ1. We also collect an
independent random sample Y1,…,Y5 from another normal population
with a known variance σ22=1 and unknown mean μ2.
We use these samples to test the hypotheses
H0:μ1=μ2 vs. H1:μ1>μ2
with a critical region of the form {X¯−Y¯>k} for some
constant k. Here Y¯ denotes the average of Yis just like X¯ denotes
the average of Xis.
(1)...
Consider a normal population distribution with the value of \(\sigma\) known.(a) What is the confidence level for the interval \(\bar{x} \pm 2.88 \sigma / \sqrt{n} ?\) (Round your answer to one decimal place.)\(\%\)(b) What is the confidence level for the interval \(\bar{x} \pm 1.47 \sigma / \sqrt{n} ?\) (Round your answer to one decimal place.) \(\%\)(c) What value of \(z_{\alpha / 2}\) in the CI formula below results in a confidence level of \(99.7 \% ?\) (Round your answer to...