A researcher wanted to test the mean of the binomial distribution as H0 : λ = 2 vs H1 : λ = 1. He decided to take two samples and he will reject the null hypothesis if both of the samples are less than 2. a) Find the type 1 error of the test b) Find the type 2 error of the test

the height of a randomly selected male individual in a population is a normal random variable with mathematical expectation m=178 σ =8 what % of the individuals of this population is taller than 185cm?the height of the female individuals in this population is of normal distribution with parameters m=165 cm and σ=7cm. what % of the women are taller than half of the men

the value used in the equation for the t-test for independent means that approximates the sample size is known as the

Let X1, X2, .. ., Xn be a random sample from a normal distribution with mean u and variance o?. Find an estimator for o? using the method of moments. Is this estimator bi- ased/unbiased? Is it consistent?

You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as µ₁ and process 2 has a mean defined as µ2. The null and alternative hypotheses are Ho: μ₁ −μ₂ ≤0 and H₁ : µ₁ −µ₂ > 0. The process variances are unknown but assumed to be equal. Using random samples of 36 observations from process 1 and 49 observations from process 2, the sample means are 60 and 50 for populations 1 and 2 respectively. Complete parts a through d below. Click the icon to view a table of critical values for the Student's t-distribution. a. Can you reject the null hypothesis, using a probability of Type I error α = 0.05, if the sample standard deviation from process 1 is 28 and from process 2 is 23? (Round to three decimal places as needed.) The test statistic is t =

We have a random variable X1 for population 1 with a mean value of 52 and standard deviation of 3. we have a random variable X2 for population 2 with a mean value of 50 and population standard deviation of 4. we obtain a random sample of 625 elements independently for both populations. what is the probability that the difference in the sample averages X1-X2 is at least 2.3?