A newly installed automatic gate system was being tested to see if the number of failures in 1,000 entry attempts was the same as the number of failures in 1,000 exit attempts. A random sample of eight delivery trucks was selected for data collection. Do these sample results show that there is a significant difference between entry and exit gate failures? Use a = 0.05. Entry failures Exit failures Truck 1 44 Truck 2 Truck 3 40 55 Truck 4 56 Truck 5 62 Truck 6 52 50 53 55 56 55 50 Truck 7 45 51 Truck 8 45 47

Periodically, customers of a financial services company are asked to evaluate the company's financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use  ? = 0.05  and test to see whether the consultant with more experience has the higher population mean service rating. Assume the population variances are unequal. Consultant A Consultant B n1 = 16 n2 = 10 x1 = 6.85 x2 = 6.25 s1 = 0.69 s2 = 0.75 (a) State the null and alternative hypotheses. -H0:?1 − ?2 = 0 Ha:?1 − ?2 = 0 -H0:?1 − ?2 > 0 Ha:?1 − ?2 = 0  -H0:?1 − ?2 ≠ 0 Ha:?1 − ?2 = 0 -H0:?1 − ?2 = 0 Ha:?1 − ?2 > 0 -H0:?1 − ?2 = 0 Ha:?1 − ?2 ≠ 0 (b) Compute the value of the test statistic. (Round your answer to three decimal places.)…

A district health officer wishes to determine if the six villages in his district are independent of residents contracting malaria, schistosomiasis, cholera or tuberculosis. Identity an appropriate statistical test and the tail of the test for the problem. Assume all samples used for study come from a normal population.

dults aged 18 years old and older were randomly selected for a survey on obesity. Adults are considered obese if their body mass index (BMI) is at least 30. The researchers wanted to determine if the proportion of southern women who are obese is less than the proportion of southern men who are obese. The results are shown in the table below. Test at the 1% level of significance.   Number who are obese Sample size Men 42,773 155,525 Women 67,176 248,775 a.State the distribution to use for the test. (Round your answers to five decimal places. b. What is the test statistic c. Conduct a Hypothesis Test

Customers of a restaurant have been complaining about food poisoning over the past week. A health professional was called to investigate. He tested a representative sample of the eggs and reported that  23%  of the sample eggs tested positive for the salmonella bacterium. If a second health professional tests 4 eggs at random, what is the mean of the number of eggs that test positive for salmonella?

An athletic shoemaker wants to test if their new running shoe specially made for sprinting is better than the competition. To do this, they recruit 35 NCAA sprinters and time their 100-meter dash wearing the company's shoe and then time their 100-meter dash again wearing the competitor’s shoe. The difference of these times is then calculated asTimecompany.shoe−Timecompetitor.shoe. The sample mean difference in times is 0.53 seconds and the sample standard deviation is 1.1. Conduct a hypothesis test at theα=0.1 level. (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in the context of the problem) (b) Calculate the test statistic (c) Calculate the critical value. (d) Draw a picture of the distribution of the test statistic underH0. Label and provide values for the critical value and the test statistic, and shade the critical region. (e) Make and justify a statistical decision at theα= 0.15 level and state your conclusions in the…

This is about ANOVA: 1. What does one-way mean? 2. What does between-subjects mean? 3. A researcher conducts a one-way ANOVA with four levels. How many different groups are in this study? 4. What are the two sources of variability for the one-way ANOVA?

The National Highway traffic Safety Administration requires each U.S. state to carry out an observational study to assess the level of seat belt use in the state. One report summarized data from a study done in a certain state. The proportions in the accompanying table are based on observations of over 25,000 drivers and passengers. Male Female Uses Seatbelt Does Not Use Seat Belt 0.42 0.455 0.08 0.045 Assume that these proportions are representative of adults in this state and that an adult from this state is selected at random. (a) What is the probability that the selected adult does not use a seat belt given that the selected individual is female? (b) What is the probability that the selected individual is female given that the selected individual does not use a seat belt? (c) Are the probabilities from parts (a) and (b) equal? Write a couple of sentences explaining why or why not. They --Select--- ✓ equal. Part (a) is the proportion of [---Select--- ---Select--- and part (b) is the…