The weight of a drug produced by a pharmaceutical company follows normal distribution. The specified variance of the weights of the drugs of this population is 0.25mg. The quality engineer of the firm claims that the variance of the weights of the drugdoes not differ significantly from the specified variance of the weights of the drug of thepopulation. So the purchase manager of a Hospital who placed order for that drug with the Pharmaceutical Company has selected a random sample of 12 drugs. The variance of theweights of the sample is found to be 0.49 mg. verify the intuition of the quality manager of Pharmaceutical Company at a significance level of 0.10.

Say you have two sets of data X1, ..., X10 and Y1,..., Y40. All of this data is considered independent. The first set of data are Normally distributed with mean B and variance 10. The second set of data are Normally distributed with mean y and variance 10. We are trying to estimate 0 = X = X; 18 + y. Consider the estimate ô = }X + Ÿ where 3 4 iX + Y where 10 vi=1 1 10 and Y = E Y;? 40 vi=1 40 (a) What is the mean, variance and distribution of 0? (b) What is the probability that 0 is larger than 1 away from 0? (c) What is the bias, variance and MSE of the estimate 0 for estimating 0?

The data from an independent-measures research study produce a sample mean difference of 4 points, and each sample has a variance of 10. If there are n = 20 scores in each sample, then what is the estimated standard error of the difference between means?

Records from previous years for a casualty insurance company show that its clients average a combined total of 1.9 auto accidents per day, with a variance of 0.31. The actuaries of the company claim that the current variance, oʻ, of the number of accidents per day is not equal to 0.31. A random sample of 17 recent days had a mean of 2 accidents per day with a variance of 0.62. If we assume that the number of accidents per day is approximately normally distributed, is there sufficient evidence to conclude, at the 0.05 level of significance, that the actuaries are correct? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p H, :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO O20 (c) Find the value of the test statistic. (Round…