Homework Answers
degree of freedom(df)=n-1=26-1=25
critical value at 98% confidence interval(t)=2.485 (use student's t table)
98% confidence interval is given as:
degree of freedom(df)=n-1=12-1=11
critical value at 99% confidence interval= 3.106 (use students t table)
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QUESTION 5 Consider a sample of size 26 from a normal distribution with mean 17.4 and...
(21) A sample of size 20 is drawn from a normal distribution with unknown variance and...
(21) A sample of size 20 is drawn from a normal distribution with unknown variance and mean. The sample variance s2 = 0.012. Find a 95% two-sided confidence interval for the standard deviation o of the population. A. [0.0833,0.1600] B. (0.010,0.0130] C. (0.0069,0.0256] D. None of the above
9.138 Consider a random sample of size 20 from a normal population with hypothesized mean 1.618. ...
9.138 Consider a random sample of size 20 from a normal population with hypothesized mean 1.618. a. Write the four parts for a one-sided, left-tailed hypothesis test concerning the population mean with α 0.05. b. Suppose x = 1.5 and s = 0.45. Find the value of the test statistic, and draw a conclusion about the population mean. c. Find the p value associated with this hypothesis test.
9.138 Consider a random sample of size 20 from a normal population...
10. Based on a random sample of size 7 from a normal distribution with mean y,...
10. Based on a random sample of size 7 from a normal distribution with mean y, a confidence interval is constructed for y. The sample standard deviation is calculated as 5.4763. Let to be the critical value of a t random variable with v degrees of freedom. The following table lists values of ta for specific combinations of a and v: v=6 v = 7 a=0.1 a = 0.05 a= 0.025 1.440 1.943 2 .447 1.4151.8952.365 If we want to...
10. Based on a random sample of size 7 from a normal distribution with mean u,...
10. Based on a random sample of size 7 from a normal distribution with mean u, a confidence interval is constructed for y. The sample standard deviation is calculated as 5.4763. Let tay be the critical value of a t random variable with v degrees of freedom. The following table lists values of ta, for specific combinations of a and v: a=0.1 1.440 1.415 a= 0.05 1.943 v=6 v=7 a= 0.025 2 .447 2.365 1.895 If we want to be...
A sample of 27 independent observations is taken from a normal distribution of unknown mean μ but...
A sample of 27 independent observations is taken from a normal distribution of unknown mean μ but known variance σ. 75.24. The sample mean is 5 is the width of the 98% confidence interval for μ? 4.42 and the sample variance is 41. What
A sample of 27 independent observations is taken from a normal distribution of unknown mean μ but known variance σ. 75.24. The sample mean is 5 is the width of the 98% confidence interval for μ?...
The random sample shown below was selected from a normal distribution. 8, 10, 6, 4, 5,...
The random sample shown below was selected from a normal distribution. 8, 10, 6, 4, 5, 3 O Complete parts a and b. a. Construct a 95% confidence interval for the population mean u. OD (Round to two decimal places as needed.) b. Assume that sample mean x and sample standard deviations remain exactly the same as those you just calculated but that are based on a sample of n = 25 observations. Repeat part a. What is the effect...
you are given For a random sample of size 13 from a normal distribution with mean...
you are given For a random sample of size 13 from a normal distribution with mean the following regarding the observations: 3 (xi – ī)2 = 77.8 The width of the 100k% confidence interval for u is 2.7005. Let to be the critical value of a t random variable with v degrees of freedom. The following table lists values of ta, for specific combinations of a and v: v = 12 v = 13 a=0.1 1.356 1.350 a= 0.07 1...
The random sample shown below was selected from a normal distribution. 7,5,9,5,7,3 Complete parts a and...
The random sample shown below was selected from a normal distribution. 7,5,9,5,7,3 Complete parts a and b. a. Construct a 99% confidence interval for the population mean . (Round to two decimal places as needed.) on b. Assume that sample mean x and sample standard deviation s remain exactly the same as those you just calculated but that are based on a sample of n 25 observations. Repeat part a. What is the effect of increasing the sample size on...
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...
11. For a random sample of size 13 from a normal distribution with mean u, you...
11. For a random sample of size 13 from a normal distribution with mean u, you are given the following regarding the observations: (ti – 1)2 = 77.8 The width of the 100% confidence interval for u is 2.7005. Let tay be the critical value of a t random variable with v degrees of freedom. The following table lists values of tay for specific combinations of a and v: v = 12 v=13 a=0.1 1.356 1.350 a= 0.07 1.580 1.572...
(21) A sample of size 20 is drawn from a normal distribution with unknown variance and mean. The sample variance s2 = 0.012. Find a 95% two-sided confidence interval for the standard deviation o of the population. A. [0.0833,0.1600] B. (0.010,0.0130] C. (0.0069,0.0256] D. None of the above
9.138 Consider a random sample of size 20 from a normal population with hypothesized mean 1.618. a. Write the four parts for a one-sided, left-tailed hypothesis test concerning the population mean with α 0.05. b. Suppose x = 1.5 and s = 0.45. Find the value of the test statistic, and draw a conclusion about the population mean. c. Find the p value associated with this hypothesis test.
9.138 Consider a random sample of size 20 from a normal population...
10. Based on a random sample of size 7 from a normal distribution with mean y, a confidence interval is constructed for y. The sample standard deviation is calculated as 5.4763. Let to be the critical value of a t random variable with v degrees of freedom. The following table lists values of ta for specific combinations of a and v: v=6 v = 7 a=0.1 a = 0.05 a= 0.025 1.440 1.943 2 .447 1.4151.8952.365 If we want to...
10. Based on a random sample of size 7 from a normal distribution with mean u, a confidence interval is constructed for y. The sample standard deviation is calculated as 5.4763. Let tay be the critical value of a t random variable with v degrees of freedom. The following table lists values of ta, for specific combinations of a and v: a=0.1 1.440 1.415 a= 0.05 1.943 v=6 v=7 a= 0.025 2 .447 2.365 1.895 If we want to be...
A sample of 27 independent observations is taken from a normal distribution of unknown mean μ but known variance σ. 75.24. The sample mean is 5 is the width of the 98% confidence interval for μ? 4.42 and the sample variance is 41. What
A sample of 27 independent observations is taken from a normal distribution of unknown mean μ but known variance σ. 75.24. The sample mean is 5 is the width of the 98% confidence interval for μ?...
The random sample shown below was selected from a normal distribution. 8, 10, 6, 4, 5, 3 O Complete parts a and b. a. Construct a 95% confidence interval for the population mean u. OD (Round to two decimal places as needed.) b. Assume that sample mean x and sample standard deviations remain exactly the same as those you just calculated but that are based on a sample of n = 25 observations. Repeat part a. What is the effect...
you are given For a random sample of size 13 from a normal distribution with mean the following regarding the observations: 3 (xi – ī)2 = 77.8 The width of the 100k% confidence interval for u is 2.7005. Let to be the critical value of a t random variable with v degrees of freedom. The following table lists values of ta, for specific combinations of a and v: v = 12 v = 13 a=0.1 1.356 1.350 a= 0.07 1...
The random sample shown below was selected from a normal distribution. 7,5,9,5,7,3 Complete parts a and b. a. Construct a 99% confidence interval for the population mean . (Round to two decimal places as needed.) on b. Assume that sample mean x and sample standard deviation s remain exactly the same as those you just calculated but that are based on a sample of n 25 observations. Repeat part a. What is the effect of increasing the sample size on...
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...
11. For a random sample of size 13 from a normal distribution with mean u, you are given the following regarding the observations: (ti – 1)2 = 77.8 The width of the 100% confidence interval for u is 2.7005. Let tay be the critical value of a t random variable with v degrees of freedom. The following table lists values of tay for specific combinations of a and v: v = 12 v=13 a=0.1 1.356 1.350 a= 0.07 1.580 1.572...
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