(b) A company produces cylindrical metal rods. The diameters of rods have a normal distribution with mean µcm and variance o² cm². A random sample of 100 rods is taken and the diameter x, in cm, of each rod is measured. The results are summarised as Ex=52.1 and r=27.303. Calculate the mean and variance of the population of the diameters of the rods (iii) Detemine a 95% confidence interval for the mean diameter of the rods. (iv) Investigate, at the 1% significance level, whether the mean diameter of the rods is 0.512 cm.

A coin-operated drink machine was designed to discharge a mean of 7 fluid ounces of coffee per cup. In a test of the machine, the discharge amounts in 16 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 6.86 fluid ounces and 0.2 fluid ounces, respectively. If we assume that the discharge amounts are approximately normally distributed, is there enough evidence, to conclude that the population mean discharge, u, differs from 7 fluid ounces? Use the 0.05 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H1. p H, :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values. (Round to…

Heavy metal concentrations from a fish sample were analyzed through Atomic Absorption Spectrophotometer (AAS). The results were obtained in the replicate samples that revealed different mercury (Hg) concentrations: 0.514 ppm, 0.503 ppm, 0.486 ppm, 0.497 ppm, and 0.472 ppm. a. Calculate the ff: (a) mean (b) standard deviation (c) variance (d) RSD (e) CV (f) Range. Show the final reported data. b. Calculate the absolute error and percent relative error of the replicate samples if the highest allowable average mercury concentration in fish per serving when eating 1 serving per week is 0.460 ppm according to Food and Drug Administration (FDA) and Environmental Protection Agency (EPA). Interpret your answer.

Let x represent the number of mountain climbers killed each,year. The long-term variance of x is approximately o Suppose that for the past 12 years, the variance has been s = 118.3. = 136.2 Use a 1% level of significance to test the claim that the recent variance for number of mountain-climber deaths is less than 136.2 Find a 90% confidence interval for the population variance. (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom?