3. Use the data from question 1. Conduct a hypothesis test at α = .05 to determine if the population variance is less than 909.00.

Question 1- 1. Consider the following sampled data: s 2 = 906.304, n = 31. Calculate the following confidence intervals for the population variance: (a) 90% (b) 95% (c) 99%

1.A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.05 in. ​(a) Determine the minimum sample size required to construct a 95​% confidence interval for the population mean. Assume the population standard deviation is 0.20 in. ​(b) Repeat part​ (a) using a population standard deviation of 0.30 in. Which standard deviation requires a larger sample​ size? Explain.

2.A soccer ball manufacturer wants to estimate the mean circumference of​ mini-soccer balls within 0.05 inch. Assume the population of circumferences is normally distributed. ​(a) Determine the minimum sample size required to construct a 95​% confidence interval for the population mean. Assume the population standard deviation is 0.30 inch. ​(b) Repeat part​ (a) using a population standard deviation of 0.40 inch. ​(c) Which standard deviation requires a larger sample​ size? Explain.

2. Using your answers from question 1, determine the following confidence intervals for the population standard deviation:

(a) 90%

(b) 95%

(c) 99%

QUESTION 1:

Question 1: 1. Consider the following sampled data: s 2 = 906.304, n = 31. Calculate the following confidence intervals for the population variance: (a) 90% (b) 95% (c) 99%

The mean of a normal probability distribution is 380; the standard deviation is 16. About 68% of the observations lie between what two values

The Food and Drug Administration (FDA) is asked to approve a new drug. The new drug should contain less than 25mg of the active ingredient “toxin”, which is assumed to have dangerous side effects. The FDA would like to restrict the error of “approving the drug despite its too high content of toxin” to a maximum risk of 5% (α ≤ 0.05). Let Xi : “ The content of toxin in the i-th pill [in mg].” ∼ N(µ, σ2 ) ∼ N(µ, 4). A simple random sample of n = 50 pills ( Xi ∼ i.i.d.) will be used for the test.

7. Given a significance level of α = 5% what is the highest probability of making a type II error?

8. In the sample, x¯ = 24.6. Compute the p-value. What do you conclude? [Write down the probability that you computed.]

9. Has a type I error occurred? Explain your answer.

10. Has a type II error occurred? Explain your answer.

(Answers are given but can you please work through the problem and show the steps)

Chapter 10 p2

Allied Corporation is trying to determine whether to purchase Machine A or B. It has leased the two machines for a month. A random sample of 5 employees has been taken. These employees have gone through a training session on both machines. Below you are given information on their productivity rate on both machines. (Let the difference d = Machine A - Machine B.)

​

Assume the population of differences is normally distributed.

A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken five years ago. Results are summarized below. Has the proportion increased significantly? Let α = .05.

A box contains 2 identical pistols. Pistol A contains 7 live bullets and 3 blank bullets while pistol B contains 3 live bullets and 7 blanks. Following a particularly annoying question in his Stat 230 class, evil Professor Moriarty chooses a pistol at random and then fires once directly at Holmes.

a. Find the probability that Holmes survives this shot (i.e. a blank bullet is fired).

b. If Holmes survives, he takes the other pistol and fires directly at Moriarty. What is the probability that Holmes survives the first shot and Moriarty survives this second shot? (i.e. a both bullets fired are blanks.).

c. If this ill-considered game continues until one of the two is shot with a live bullet, what is the probability that the person who survives is Holmes?

(Answers are given but could you please work through the problem and show me the steps?)

Chapter 9

Understand the difference between type I and type II errors.

Establish null and alternative hypotheses

The average U.S. daily internet use at home is two hours and twenty minutes. A sample of 64 homes in Soddy-Daisy showed an average usage of two hours and 50 minutes with a standard deviation of 80 minutes. We are interested in determining whether or not the average usage in Soddy-Daisy is significantly different from the U.S. average.

The Bureau of Labor Statistics reported that the average yearly income of dentists in the year 2012 was $110,000. A sample of 81 dentists, which was taken in 2013, showed an average yearly income of $120,000. Assume the standard deviation of the population of dentists’s incomes in 2012 is $36,000.

When doing an experiment, the experimenter wants increase the chances that subjects' characteristics, that could bias the results of the experiment, and reduce the validity of the findings, are equally distributed across the treatment groups. Which of the following procedures would the experimenter utilize to accomplish this purpose?

a) random assignment b) systematic assignment c) reliable assignment d) all of the above

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 15. Find the probability that a randomly selected adult has an IQ less than 115.

(Answers are given but could you please work through the problem and show me the steps?)

Chapter 8

A local health center noted that in a sample of 400 patients, 80 were referred to them by the local hospital.

A simple random sample of 36 items resulted in a sample mean of 40 and a standard deviation of 12. Construct a 95% confidence interval for the population mean.

Six hundred consumers belonging to the 25-34 age group were randomly selected in a city and were asked whether they would like to purchase a domestic or a foreign automobile. Their responses are given below.

​

Develop a 95% confidence interval for the proportion of all such consumers who prefer to purchase domestic automobiles.

1. Assume that a sample is used to estimate a population proportion p. Find the 99.9% confidence interval for a sample of size 159 with 40% successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.

C.I. =

An economist with the Liquor, Hospitality and Miscellaneous Workers' Union collected data on the weekly salaries of workers in the hospitality industry in Cairns and Townsville. The union believed that the weekly salaries of employees in Cairns were higher and they were mounting a case for the equalisation of salaries between the northern cities. The researcher took samples of size 30 and 37 in Cairns and Townsville, respectively, and found that the average and standard deviation of the weekly salaries were $585.43 and $38.72 respectively in Townsville, and $616.19 and $29.13 in Cairns. Use Cairns minus Townsville.

1. Determine a point estimate for the value of the difference in average weekly salary between the two groups (in dollars to 2 decimal places).

2. Calculate the standard error for the difference between the means assuming that the workers' salaries in both locations are normally distributed and have the same population variance (in dollars to 2 decimal places).   

3. Use Kaddstat to determine a 95% confidence interval for the difference between the average weekly salaries in Cairns and Townsville. lower limit   
upper limit   (in dollars to 2 decimal places