Exam 13: Introduction to Inference

A company manufactures U-100 insulin syringes designed to contain 1 milliliter (ml) of a solution containing insulin. The actual distribution of solution volumes in these syringes is Normal, with mean? and standard deviation ?= 0.05 ml. We randomly select 8 syringes and measure the volume of solution in each. The results of these 8 measurements (in ml) are as follows: ? 1.05 1.04 1.06 1.01 0.98 0.98 1.03 0.99 Do these data give evidence that the true population mean solution volume is not 1 m1? What is the P-value for the appropriate null and alternative hypotheses?

The scores of a certain population on the Wechsler Intelligence Scale for Children IV (WISC IV) are thought to be Normally distributed, with mean μ and standard deviation σ= 15. Bill is a child psychologist who obtains a simple random sample of 25 children from this population; each child is given the WISC IV. Suppose a histogram of the 25 WISC scores is the following: Bill calculates a 95% confidence interval for μ and finds it to be (98.42, 110.20). What should Bill conclude about the 95% confidence interval?

A medical researcher treats 100 subjects with high cholesterol levels with a new drug. The average decrease in cholesterol level is x̄= 80 after two months of taking the drug. Assume that the decrease in cholesterol after two months of taking the drug follows a Normal distribution, with unknown mean μ and standard deviation σ= 20. What is the 90% confidence interval for μ based on these data?

When does a level α two-sided significance test reject the null hypothesis H₀: μ= μ₀?

Twenty-five patients at a large clinic volunteer to participate in a study focusing on weight loss. These 25 patients had a mean weight loss score of x̄= 4500 g over two weeks. Suppose we know that the standard deviation of the population of weight changes on this particular diet is σ= 100 g. Assume the population of weight losses is approximately Normally distributed. What is a 90% confidence interval for the mean weight loss μ for the population, based on the collected data?

The level of nitrogen oxides (NO_x) in the exhaust of cars of a particular model varies Normally, with standard deviation σ= 0.05 gram per mile (g/mi). A random sample of 12 cars of this particular model is taken and is found to have a mean NO_x emission of x̄= 0.298 g/mi. Government regulations call for NO_x emissions no higher than 0.3 g/mi. Do the data provide evidence that this particular model meets the government regulation? What should you conclude from these data?

A certain population follows a Normal distribution with mean μ and standard deviation σ= 2.5. You collect data and test the following hypotheses: H₀: μ= 1 versus H_a: μ≠1 You obtain a P-value of 0.022. Which of the following statements is TRUE?

The level of nitrogen oxides (NO_x) in the exhaust of cars of a particular model varies Normally, with standard deviation σ= 0.05 gram per mile (g/mi). A random sample of 12 cars of this particular model is taken and is found to have a mean NO_x emission of x̄= 0.298 g/mi. Government regulations call for NO_x emissions no higher than 0.3 g/mi. Do the data provide evidence that this particular model meets the government regulation? What is the P-value for the appropriate null and alternative hypotheses?