esting: H0:μ≥13H0:μ≥13 H1:μ<13H1:μ<13 Your sample consists of 43 values, with a sample mean of 12.9. Suppose the population standard deviation is known to be 2.01. a) Calculate the value of the test statistic, rounded to 2 decimal places. z=z= b) At α=0.02α=0.02, the rejection region is z>2.33z>2.33 z<-2.33z<-2.33 z<-2.33orz>2.33z<-2.33orz>2.33 z>2.05z>2.05 z<-2.05z<-2.05 z<-2.05orz>2.05z<-2.05orz>2.05 c) The decision is to Fail to reject the null hypothesis Accept the null hypothesis Accept the alternative hypotheis Reject the null hypothesis

We collected a sample of twenty-five observations. We assumed that the observations are from a population whose values follow a normal distribution with a mean of u and a standard deviation of five. We performed a test with these hypotheses Ho: μ = 0H₁ = 0 and H₁ : μ0H₁0. The test statistic is the sample mean . The 5% rejection region is 1.959964 > 1.959964. What is the power of this test when μ = -2μ = -2? Please state the statistical power up to the fourth decimal place.

A random sample of  n1 = 49  measurements from a population with population standard deviation  ?1 = 3  had a sample mean of  x1 = 10.  An independent random sample of  n2 = 64  measurements from a second population with population standard deviation  ?2 = 4  had a sample mean of  x2 = 12.  Test the claim that the population means are different. Use level of significance 0.01. (a) Check Requirements: What distribution does the sample test statistic follow? Explain. The Student's t. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations.    The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. (b) State the hypotheses. H0: ?1 = ?2;…

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A population of values has a normal distribution with μ=184.5μ=184.5 and σ=15.5σ=15.5. You intend to draw a random sample of size n=68n=68.Find P40, which is the mean separating the bottom 40% means from the top 60% means.P40 (for sample means) = Enter your answers as numbers accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

H0:μ=41.92H0:μ=41.92H1:μ≠41.92H1:μ≠41.92Your sample consists of 43 subjects, with a mean of 42 and standard deviation of 1.56.Calculate the test statistic, rounded to 2 decimal places. t=

H0:μ=38.935H0:μ=38.935H1:μ≠38.935H1:μ≠38.935Your sample consists of 31 subjects, with a mean of 38.5 and standard deviation of 4.13.Calculate the test statistic, rounded to 2 decimal places. t=t=

The data set of the diameters of the metal cylinders manufactured an automatic machine has sample size of n=28, mean of x= 49.94 mm and std. of S = 0.15 mm. Expected diameter of metal cylinder is µ = 50.00 mm. Can we be 95% confident that machine calibrated properly?