Which of the following statements is true? The t-distribution with 1 degree of freedom is equivalent...
Which of the following statements is true?
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The t-distribution with 1 degree of freedom is equivalent to the standard normal distribution. |
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When division by a factor of n-1 is used, the sample variance s2 is an unbiased estimator of the population variance σ2. |
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If a hypothesis test is conducted at the 5% significance level, then a p-value of 0.087 would lead the researcher to reject H0. |
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A 99% z-based confidence interval of the population mean μ based on a sample will be narrower than a 95% z-based confidence interval of the population mean μ based on the same sample. |
Homework Answers
Following statement is correct
A 99% z-based confidence interval of the population mean μ based on a sample will be narrower than a 95% z-based confidence interval of the population mean μ based on the same sample.
Confidence interval formula is given as follows
Width of confidence interval will be larger if Z score will be larger. Z score is directly proportional to confidence level. Hence last statement is correct.
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Which of the following statements is true?
The t-distribution with 1 degree of freedom is
equivalent...
1. (40) Suppose that X1, X2, Xn forms an independent and identically distributed sample from a normal distribution with mean μ and variance σ2, both unknown: 2nơ2 (a) Derive the sample variance, S2,...
1. (40) Suppose that X1, X2, Xn forms an independent and identically distributed sample from a normal distribution with mean μ and variance σ2, both unknown: 2nơ2 (a) Derive the sample variance, S2, for this random sample. (b) Derive the maximum likelihood estimator (MLE) of μ and σ2 denoted μ and σ2, respectively. (c) Find the MLE of μ3 (d) Derive the method of moment estimator of μ and σ2, denoted μΜΟΜΕ and σ2MOME, respectively (e) Show that μ and...
6. Consider the following sample: Xi = -2, X2 = 12. X7-1.5, Xs -0.5, a. Estimate the population mean, μ, using an analogical estimator. b. Estimate the population variance. ơ2, using a biased and an...
6. Consider the following sample: Xi = -2, X2 = 12. X7-1.5, Xs -0.5, a. Estimate the population mean, μ, using an analogical estimator. b. Estimate the population variance. ơ2, using a biased and an unbiased estimator. c. Assuming that the random sample is drawn from a normal population with known variance, σ2-4, construct a 95% confidence interval for the population mean. d. Assuming that the random sample is drawn from a normal population with unknown variance, σ2, construct a...
True or False? The higher the confidence level, the narrower is the confidence interval for the...
True or False? The higher the confidence level, the narrower is the confidence interval for the mean. Select an answer The most efficient point estimator for the population mean ù is the sample median . Select an answer • To reduce the width of a confidence interval, we can increase the sample size n. Select an answer • As long as the population is normal with variance o’, the statistic (n-1) S2 has a Chi-squared 02 distribution with n degrees...
1. Select all true statements about sample mean and sample median. A) When the population distribution...
1. Select all true statements about sample mean and sample median. A) When the population distribution is skewed, sample mean is biased but sample median is an unbiased estimator of population mean. B) When the population distribution is symmetric, both mean and sample median are unbiased estimators of population mean. C) Sampling distribution of sample mean has a smaller standard error than sample median when population distribution is normal. D) Both mean and median are unbiased estimators of population mean...
1) For the t distribution with 16 degrees of freedom, find the value for which the...
1) For the t distribution with 16 degrees of freedom, find the value for which the upper tail area is 0.005. 2) For the t distribution with 13 degrees of freedom, calculate P(T < 1.771). 3) In order to estimate the average electric usage per month, a sample of 45 houses were selected and the electric usage determined. The sample mean is 2,000 KWH. Assume a population standard deviation of 101 kilowatt hours. At 90% confidence, compute the margin of...
A new diet that promises a fast loss of weight is launched. The change in weight after a week on the diet is modelled using a Normal distribution with mean u and variance σ2. Let z, . . . , zn be an...
A new diet that promises a fast loss of weight is launched. The change in weight after a week on the diet is modelled using a Normal distribution with mean u and variance σ2. Let z, . . . , zn be an independent sample from this Normal. (a) Knowing that μ z, find the method of moments estimator for σ. [4] (b) State (without deriving) an alternative estimator you know for σ2. Give one reason why one would prefer...
(4 points) Let Xi, , Xn denote a randon sample from a Normal N(μ, 1) distribution, with 11 as the...
please answer with full soultion. with explantion.
(4 points) Let Xi, , Xn denote a randon sample from a Normal N(μ, 1) distribution, with 11 as the unknown parameter. Let X denote the sample mean. (Note that the mean and the variance of a normal N(μ, σ2) distribution is μ and σ2, respectively.) Is X2 an unbiased estimator for 112? Explain your answer. (Hint: Recall the fornula E(X2) (E(X)Var(X) and apply this formula for X - be careful on the...
Suppose that Y1 , Y2 ,..., Yn denote a random sample of size n from a...
Suppose
that Y1 , Y2 ,..., Yn denote a random sample of size n from a
normal population with mean μ and variance 2 .
Problem # 2: Suppose that Y , Y,,...,Y, denote a random sample of size n from a normal population with mean u and variance o . Then it can be shown that (n-1)S2 p_has a chi-square distribution with (n-1) degrees of freedom. o2 a. Show that S2 is an unbiased estimator of o. b....
If a null hypothesis is rejected at a significance level of 1%, then we should say...
If a null hypothesis is rejected at a significance level of 1%,
then we should say that it was rejected at 1%. Reporting that the
null was also rejected at the 5% level of significance is
unnecessary and unwise.
True
False
The p-value equals alpha, the level of significance of the
hypothesis test.
True
False
THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING
INFORMATION:
Let X1, X2,
X3, and X4 be a random
sample of observations from a population with...
12. As the number of degrees ot trdom ort d n s the the t distribution...
12. As the number of degrees ot trdom ort d n s the the t distribution andd the standard nomal dist becomes larger b becomes smalter stays the same huctuates. d. 13. In interval esionation, thet distribution is applicatle ondy when a. the population has a mean of tess than 30 b. the sample standard deviation is used to estimate the population standard deviation the variance of the population is known d. the mean of the population is unknown. C....
1. (40) Suppose that X1, X2, Xn forms an independent and identically distributed sample from a normal distribution with mean μ and variance σ2, both unknown: 2nơ2 (a) Derive the sample variance, S2, for this random sample. (b) Derive the maximum likelihood estimator (MLE) of μ and σ2 denoted μ and σ2, respectively. (c) Find the MLE of μ3 (d) Derive the method of moment estimator of μ and σ2, denoted μΜΟΜΕ and σ2MOME, respectively (e) Show that μ and...
6. Consider the following sample: Xi = -2, X2 = 12. X7-1.5, Xs -0.5, a. Estimate the population mean, μ, using an analogical estimator. b. Estimate the population variance. ơ2, using a biased and an unbiased estimator. c. Assuming that the random sample is drawn from a normal population with known variance, σ2-4, construct a 95% confidence interval for the population mean. d. Assuming that the random sample is drawn from a normal population with unknown variance, σ2, construct a...
True or False? The higher the confidence level, the narrower is the confidence interval for the mean. Select an answer The most efficient point estimator for the population mean ù is the sample median . Select an answer • To reduce the width of a confidence interval, we can increase the sample size n. Select an answer • As long as the population is normal with variance o’, the statistic (n-1) S2 has a Chi-squared 02 distribution with n degrees...
A new diet that promises a fast loss of weight is launched. The change in weight after a week on the diet is modelled using a Normal distribution with mean u and variance σ2. Let z, . . . , zn be an independent sample from this Normal. (a) Knowing that μ z, find the method of moments estimator for σ. [4] (b) State (without deriving) an alternative estimator you know for σ2. Give one reason why one would prefer...
please answer with full soultion. with explantion.
(4 points) Let Xi, , Xn denote a randon sample from a Normal N(μ, 1) distribution, with 11 as the unknown parameter. Let X denote the sample mean. (Note that the mean and the variance of a normal N(μ, σ2) distribution is μ and σ2, respectively.) Is X2 an unbiased estimator for 112? Explain your answer. (Hint: Recall the fornula E(X2) (E(X)Var(X) and apply this formula for X - be careful on the...
Suppose
that Y1 , Y2 ,..., Yn denote a random sample of size n from a
normal population with mean μ and variance 2 .
Problem # 2: Suppose that Y , Y,,...,Y, denote a random sample of size n from a normal population with mean u and variance o . Then it can be shown that (n-1)S2 p_has a chi-square distribution with (n-1) degrees of freedom. o2 a. Show that S2 is an unbiased estimator of o. b....
If a null hypothesis is rejected at a significance level of 1%,
then we should say that it was rejected at 1%. Reporting that the
null was also rejected at the 5% level of significance is
unnecessary and unwise.
True
False
The p-value equals alpha, the level of significance of the
hypothesis test.
True
False
THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING
INFORMATION:
Let X1, X2,
X3, and X4 be a random
sample of observations from a population with...
12. As the number of degrees ot trdom ort d n s the the t distribution andd the standard nomal dist becomes larger b becomes smalter stays the same huctuates. d. 13. In interval esionation, thet distribution is applicatle ondy when a. the population has a mean of tess than 30 b. the sample standard deviation is used to estimate the population standard deviation the variance of the population is known d. the mean of the population is unknown. C....
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