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Suppose that the underlying distribution is approximately normal but with unknown variance. You would like to...
6. Suppose we observe Y,... Yn from a normal distribution with unknown parameters such that Y...
6. Suppose we observe Y,... Yn from a normal distribution with unknown parameters such that Y 24, s2 36, and n 15. (a) Find the rejection region of a level α-0.05 test of H0 : μ-20 vs. H1 : μ * 20. Would this test reject with the given data? (b) Find the rejection region of a level α -0.05 test of Ho : μ < 20 vs. H1 : μ > 20 would this test reject with the given...
6. Let Xi 1,... ,Xn be a random sample from a normal distribution with mean u and variance ơ2 whi...
6. Let Xi 1,... ,Xn be a random sample from a normal distribution with mean u and variance ơ2 which are both unknown. (a) Given observations xi, ,Xn, one would like to obtain a (1-a) x 100% one-sided confidence interval for u as a form of L E (-00, u) the expression of u for any a and n. (b) Based on part (a), use the duality between confidence interval and hypothesis testing problem, find a critical region of size...
A sample from a Normal distribution with an unknown mean u and known variance o =...
A sample from a Normal distribution with an unknown mean u and known variance o = 45 was taken with n=9 samples giving sample mean of y = 3.6. (a) Construct a Hypothesis test with significance level a = 0.05 to test whether the mean is equal to 0 or it is greater than 0. What can you conclude based on the outcome of the sample? (b) Calculate the power of this test if the true value of the mean...
1 For the hypothesis test H0 mu<=5 against H1: mu >5 with variance unknown and n=11,...
1 For the hypothesis test H0 mu<=5 against H1: mu >5 with variance unknown and n=11, find the best approximation for the P-value for the test statistic t0=1.945. 0.25 ≤ p ≤ 0.50 0.10 ≤ p ≤ 0.25 0.010 ≤ p ≤ 0.025 0.025 ≤ p ≤ 0.050 0.0025 ≤ p ≤ 0.0050 2 The probability of type II error increases if the difference between the hypothesized values of the parameter increases, assuming that the sample size and other parameters...
In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of...
In this problem, assume that the distribution of differences is
approximately normal. Note: For degrees of freedom
d.f. not in the Student's t table, use
the closest d.f. that is smaller. In
some situations, this choice of d.f. may increase
the P-value by a small amount and therefore produce a
slightly more "conservative" answer.
A survey of houses and traditional hogans was made in a number of
different regions of the modern Navajo Indian Reservation. The
following table is the...
Ms. Lisa Monnin is the budget director for Nexus Media Inc. She would like to compare...
Ms. Lisa Monnin is the budget director for Nexus Media Inc. She
would like to compare the daily travel expenses for the sales staff
and the audit staff. She collected the following sample
information.
Sales
($)
129
135
148
160
135
144
Audit ($)
122
103
127
136
129
120
142
At the 0.025 significance level, can she conclude that the mean
daily expenses are greater for the sales staff than the audit
staff?
Click here for the Excel Data...
Problem 1: Medicare would like to test the hypothesis that the average monthly rate for one-bedroom...
Problem 1: Medicare would like to test the hypothesis that the average monthly rate for one-bedroom assisted-living facility is equal to $3,300. A random sample of 12 assisted-living facilities had an average rate of $3,690 per month. The standard deviation for this sample was $530. Medicare would like to set α = 0.05. The correct hypothesis statement for this hypothesis test would be H0: μ ≥ $3,300; H1: μ < $3,300. H0: μ = $3,300; H1: μ ≠ $3,300. H0:...
6. (4 points) Suppose n = 82. How much is σˆ 2 , the estimated variance...
6. (4 points) Suppose n = 82. How much is σˆ 2 , the estimated
variance of the error term ui?
A. 0.00625
B. 0.0125
C. 0.025
D. 0.05
7. (4 points) Suppose βˆ 1 = 0.75, SE(βˆ 1) = 0.01 and n = 52.
Then the 90% confidence interval for βˆ 1 would be
A. [0.4224, 1.1994]
B. [0.6112, 0.9112]
C. [0.7336, 0.7664]
D. [0.7229, 0.7661]
8. (4 points) Suppose one tested and rejected the null
hypothesis H0 :...
6. Suppose we obeerve Yi,...Yn from a normal distribution with unknown parameters such that Y 24,...
6. Suppose we obeerve Yi,...Yn from a normal distribution with unknown parameters such that Y 24, 236, and (a) Find the rejection region of a level a-0.05 test of Ho : μ-20 vs. Hi :"t 20. Would this test reject with the (b) Find the rejection region of a level α-0.05 test of Ho : μ 20 vs. H: μ > 20, would this test reject with the given data? given data? (c) Will the p-value for the given data...
I would like the whole Question done on r studio with the R Code. 1. In...
I would like the whole Question done on r studio with
the R Code.
1. In this question we will evaluate type I and type II error probabilities for one-sided tests. We will consider normally distributed data, with unit variance and independent obervations. We will use Ho : μ-0 for the null and H1 : μ-1 for the alternative, unless otherwise stated. (a) Suppose we have n-6 observationsx. What is the sampling distribution of the (10 marks) sample mean (that...
6. Suppose we observe Y,... Yn from a normal distribution with unknown parameters such that Y 24, s2 36, and n 15. (a) Find the rejection region of a level α-0.05 test of H0 : μ-20 vs. H1 : μ * 20. Would this test reject with the given data? (b) Find the rejection region of a level α -0.05 test of Ho : μ < 20 vs. H1 : μ > 20 would this test reject with the given...
6. Let Xi 1,... ,Xn be a random sample from a normal distribution with mean u and variance ơ2 which are both unknown. (a) Given observations xi, ,Xn, one would like to obtain a (1-a) x 100% one-sided confidence interval for u as a form of L E (-00, u) the expression of u for any a and n. (b) Based on part (a), use the duality between confidence interval and hypothesis testing problem, find a critical region of size...
A sample from a Normal distribution with an unknown mean u and known variance o = 45 was taken with n=9 samples giving sample mean of y = 3.6. (a) Construct a Hypothesis test with significance level a = 0.05 to test whether the mean is equal to 0 or it is greater than 0. What can you conclude based on the outcome of the sample? (b) Calculate the power of this test if the true value of the mean...
In this problem, assume that the distribution of differences is
approximately normal. Note: For degrees of freedom
d.f. not in the Student's t table, use
the closest d.f. that is smaller. In
some situations, this choice of d.f. may increase
the P-value by a small amount and therefore produce a
slightly more "conservative" answer.
A survey of houses and traditional hogans was made in a number of
different regions of the modern Navajo Indian Reservation. The
following table is the...
Ms. Lisa Monnin is the budget director for Nexus Media Inc. She
would like to compare the daily travel expenses for the sales staff
and the audit staff. She collected the following sample
information.
Sales
($)
129
135
148
160
135
144
Audit ($)
122
103
127
136
129
120
142
At the 0.025 significance level, can she conclude that the mean
daily expenses are greater for the sales staff than the audit
staff?
Click here for the Excel Data...
6. (4 points) Suppose n = 82. How much is σˆ 2 , the estimated
variance of the error term ui?
A. 0.00625
B. 0.0125
C. 0.025
D. 0.05
7. (4 points) Suppose βˆ 1 = 0.75, SE(βˆ 1) = 0.01 and n = 52.
Then the 90% confidence interval for βˆ 1 would be
A. [0.4224, 1.1994]
B. [0.6112, 0.9112]
C. [0.7336, 0.7664]
D. [0.7229, 0.7661]
8. (4 points) Suppose one tested and rejected the null
hypothesis H0 :...
6. Suppose we obeerve Yi,...Yn from a normal distribution with unknown parameters such that Y 24, 236, and (a) Find the rejection region of a level a-0.05 test of Ho : μ-20 vs. Hi :"t 20. Would this test reject with the (b) Find the rejection region of a level α-0.05 test of Ho : μ 20 vs. H: μ > 20, would this test reject with the given data? given data? (c) Will the p-value for the given data...
I would like the whole Question done on r studio with
the R Code.
1. In this question we will evaluate type I and type II error probabilities for one-sided tests. We will consider normally distributed data, with unit variance and independent obervations. We will use Ho : μ-0 for the null and H1 : μ-1 for the alternative, unless otherwise stated. (a) Suppose we have n-6 observationsx. What is the sampling distribution of the (10 marks) sample mean (that...
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