Question

Hypothesis Testing Example 7: Steps in Hypothesis Testing: A manufacturer claims that the thickness of the spearmint gum it produces is 7.5 one- hundredths of an inch. A quality control specialist regularly checks this claim. On one production run, he took a random sample of n= 10 pieces of gum and measured their thickness. The quality control specialist's hypotheses are: HO: 1. Step 1: State Hypotheses 2. Step 2: Select alpha, Draw Picture, Label Critical Values and Rejection Region(s) 3. Step 3: Select Test Statistic 4. Step 4: State Decision Rule 5. Step 5: Calculate Test Statistic, Make Decision 6. Step 6: Take Action; State what the results mean Example 8: Consider the population of many adults. A researcher hypothesized that the average adult body temperature is lower than the often-advertised 98.6 degrees F. That is, the researcher wants an answer to the question: "Is the average adult body temperature 98.6 degrees? Or is it lower?" To answer his research question, the researcher starts by assuming that the average adult body temperature was 98.6 degrees F. Then, the researcher went out and tried to find evidence that refutes his initial assumption. In doing so, he selects a random sample of 130 adults. The average body temperature of the 130 sampled adults is 98.25 degrees. HO: Example 1: According to a website, the average price charged to a customer to have a 12 by 18 wall-to-wall carpet shampoo cleaning is about $50. Suppose that a start-up company believes that in the region that they operate, the average price is higher. To test this hypothesis, the company randomly contacts 23 customers who have recently had a 12 by 18 wall-to-wall carpet shampoo cleaning and asked the customers how much they were charged for the job. Suppose the resulting data are given below and that the population standard deviation price is $3.49. Use a 10% level of significance to test their hypothesis. Explain Type I and Il errors in the context of the problem. I = $52.17 n=23 O= $3-49a .10 HA: Example 9: Newborn babies are more likely to be boys than girls. A random sample found 13,173 boys were born among 25,468 newborn children. The sample proportion of boys was 0.5172. Is this sample evidence that the birth of boys is more common than the birth of girls in the entire population? Example 2: Suppose that in the past years the average price per square foot for warehouses in the U.S. has been $32.28. A national real estate investor wants to determine whether the figure has changed now. The investor hires a researcher who randomly samples 49 warehouses that are for sale across the U.S. and finds that the mean price per square foot is $31.67, with a standard deviation of $1.29. Assume that the prices of warehouses footage are normally distributed in the population. If the researcher uses a 5% level of significance, what statistical conclusion can be reached? Explain Type land Il errors in the context of the problem. Here, we want to test HO НА Example 3: A large manufacturing company investigated the service it received from suppliers and discovered that, in the past, 32% of all materials shipments were received late. However, the company recently installed a just-in-time system in which suppliers are linked more closely to the manufacturing process. A random sample of 118 deliveries since the just-in-time system was installed reveals that 22 deliveries were late. Use this sample information to test whether the proportion of late deliveries was reduced significantly. Let a=.05. Explain Type I and Il errors in the context of the problem.

Answer 1

07. Ho: M = 7.5 THAIME 7,5 HOP=0.50 HA: P>0.50 Hoi l = 9806 °F Hai H< 98.6°F where po is the proportion of boys.