A single observation X from a normal population is used to test the null hypothesis H0:(μ=2,σ2=4)...

A single observation X from a normal population is used to test the null hypothesis H0:(μ=2,σ2=4) against H1:(μ=1,σ2=2).

Construct the most powerful critical region of size α=0.05 for this test.

Expert Solution

orchestra answered 2 years ago

For a two-tailed hypothesis test at the significance level alpha, the null hypothesis H0: μ =...

For a two-tailed hypothesis test at the significance level alpha, the null hypothesis H0: μ = μ0 will be rejected in favor of the alternative hypothesis Ha: μ≠ μ0 if and only if μ0 lies outside the (1 - α) level confidence interval for μ. Illustrate the preceding relationship by obtaining the appropriate one-mean z-interval for the data below. Suppose the mean height of women age 20 years or older in a certain country is 62.8 inches. One hundred randomly...

A test of the null hypothesis H0: μ = μ0 gives test statistic z = −0.45....

A test of the null hypothesis H0: μ = μ0 gives test statistic z = −0.45. (Round your answers to four decimal places.) (a) What is the P-value if the alternative is Ha: μ > μ0? (b) What is the P-value if the alternative is Ha: μ < μ0? (c) What is the P-value if the alternative is Ha: μ ≠ μ0?

A t statistic was used to conduct a test of the null hypothesis H0: µ =...

A t statistic was used to conduct a test of the null hypothesis H0: µ = 11 against the alternative Ha: µ ≠ 11, with a p-value equal to 0.042. A two-sided confidence interval for µ is to be considered. Of the following, which is the largest level of confidence for which the confidence interval will NOT contain 11? A 90% confidence level A 92% confidence level A 96% confidence level A 97% confidence level A 98% confidence level

2.In a test of the hypothesis H0: μ = 50 versus Ha: μ < 50, a...

2.In a test of the hypothesis H0: μ = 50 versus Ha: μ < 50, a sample of 40 observations is selected from a normal population and has a mean of 49.0 and a standard deviation of 4.1. a) Find the P-value for this test. b) Give all values of the level of significance α for which you would reject H0. 3.In a test of the hypothesis H0: μ = 10 versus Ha: μ≠ 10, a sample of 16 observations...

Consider a general one-sided hypothesis test on a population mean µ with null hypothesis H0 :...

Consider a general one-sided hypothesis test on a population mean µ with null hypothesis H0 : µ = 0, alternative hypothesis Ha : µ > 0, and Type I Error α = 0.02. Assume that using a sample of size n = 100 units, we observe some positive sample mean x > 0 with standard deviation s = 5. (a) Calculate the Type II Error and the power of the test assuming the following observed sample means: (i) x =...

Let X ∼ Normal(μ = 20, σ2 = 4). (a) Give the mgf MX of X....

Let X ∼ Normal(μ = 20, σ2 = 4). (a) Give the mgf MX of X. (b) Find the 0.10 quantile of X. (c) Find an interval within which X lies with probability 0.60. (d) Find the distribution of Y = 3X −10 by finding the mgf MY of Y

Suppose you reject the null hypothesis H0: μ = 58. It turns out the population mean...

Suppose you reject the null hypothesis H0: μ = 58. It turns out the population mean is actually equal to 55. You have made A. Type I and Type II errors B. the correct decision C. a Type I error D. a Type II error We have created a 97% confidence interval for μ with the result [57, 97]. If we test H0: μ=98 versus H1: μ≠ 98 at a level of significance of 0.03 then our conclusion would be:...

Test the null hypothesis H0:μ=3.8against the alternative hypothesis HA:μ<3.8, based on a random sample of 25...

Test the null hypothesis H0:μ=3.8against the alternative hypothesis HA:μ<3.8, based on a random sample of 25 observations drawn from a normally distributed population with x¯=3.6 and σ=0.72. a) What is the value of the test statistic? Round your response to at least 3 decimal places. b) What is the appropriate p-value? Round your response to at least 3 decimal places. c) Is the null hypothesis rejected at: i) the 10% level of significance? YesNoClick for List ii) the...

Test the null hypothesis H0:μ=3.8against the alternative hypothesis HA:μ≠3.8, based on a random sample of 35...

Test the null hypothesis H0:μ=3.8against the alternative hypothesis HA:μ≠3.8, based on a random sample of 35 observations drawn from a normally distributed population with x¯=4 and σ=0.89. a) What is the value of the test statistic? Round your response to at least 3 decimal places. b) What is the appropriate p-value? Round your response to at least 3 decimal places. c) Is the null hypothesis rejected at: i) the 5% level of significance? NoYesClick for List ii) the...

Test the null hypothesis H0:μ=3.3against the alternative hypothesis HA:μ≠3.3, based on a random sample of 37...

Test the null hypothesis H0:μ=3.3against the alternative hypothesis HA:μ≠3.3, based on a random sample of 37 observations drawn from a normally distributed population with x¯=3.5 and σ=0.89. a) What is the value of the test statistic? Round your response to at least 3 decimal places. b) What is the appropriate p-value? Round your response to at least 3 decimal places. c) Is the null hypothesis rejected at: i) the 5% level of significance? YesNoClick for List ii) the...

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