In a chemical process, the amount of a certain type of impurity in the output is difficult to control and is thus a random variable. Speculation is that the population mean amount of the impurity is 0.20 gram per gram of output. It is known that the standard deviation is 0.1 gram per gram. An experiment is conducted to gain more insight regarding the speculation that μ = 0.2. The process is run on a lab scale 50 times and the sample average ¯x turns out to be 0.23 gram per gram. Comment on the speculation that the mean amount of impurity is 0.20 gram per gram. Make use of the Central Limit Theorem in your work.

In 2006, the Arundel County Maryland Department of Health tested local wells for elevated levels of arsenic. They found that 35 out of 71 wells showed elevated levels. Atomic  Absorption Spectroscopy is a very convenient way to measure arsenic in water. Imagine you are a lab manager and you have given identical arsenic samples (n = 10) to two different technicians. The first technician determines his sample has a standard deviation of 0.015 while the second technician reports a standard deviation of 0.033.  Construct a 90% confidence interval for the ratio of the sample standard deviations. Assume the population source data is normally distributed. Enter your answer using interval notation.

There are many situations in which we want to compare means from populations having standard deviations that are equal. This method applies even if the standard deviations are known to be only approximately equal. Consider a report regarding average incidence of fox rabies in two regions. For region I, n1 = 16, x1 ≈ 4.73, and s1 = 2.84 and for region II, n2 = 15, x2 ≈ 3.93, and s2 = 2.45. The two sample standard deviations are sufficiently close that we can assume ?1 = ?2. Use the method of pooled standard deviation to consider the report, testing if there is a difference in population mean average incidence of rabies at the 5% level of significance. (Round your answer to three decimal places.) t =

Solve question 9, Part A, Part B and Part C only.

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.6 parts/million (ppm). A researcher believes that the current ozone level is at an excess level. The mean of 14 samples is 4.9 ppm with a variance of 1.2 Does the data support the claim at the 0.01 level? Assume the population distribution is approximately normal. Step 2 of 5 :   Find the value of the test statistic. Round your answer to three decimal places.

Part 1 of 4 Suppose that you randomly survey death records for people born in 1900 in Virginia and compared the life span of two different ethnicities. Of the 132 individuals sampled from ethnicity 1, the mean life span was 58.5 years with a standard deviation of 16.9 years. Of the 191 individuals sampled from ethnicity 2, the mean life span was 54.3 years with a standard deviation of 10.3 years. Conduct a hypothesis test with a 7% level of significance to see if the mean life spans in Virginia were the same for the two ethnicities. Step 1: State the null and alternative hypotheses. Ho: 12V✓0 Ha: 1₂V0 (So we will be performing a two-tailed Part 2 of 4 Step 2: Assuming the null hypothesis is true, determine the features of the distribution of the differences of sample means. The differences of sample means are t-distributed and distribution standard deviation Question Help: Post to forum C Submit Part test.) 06 ✓✓with distribution mean MacBook Pro Search or type URL ...........

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 88 and standard deviation σ = 21. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) (a) x is more than 60(b) x is less than 110(c) x is between 60 and 110(d) x is greater than 140 (borderline diabetes starts at 140)