In Example 23.3 Chapter 23 of the textbook, we tested whether the average fat lost from 1 year of dieting versus 1 year of exercise was equivalent. The study also measured lean body weight (muscle) lost or gained. The average for the 47 men who exercised was a gain of 0.1 kg, which can be thought of as a loss of –0.1 kg. The standard deviation was 2.2 kg. For the 42 men in the dieting group, there was an average loss of 1.3 kg, with a standard deviation of 2.6 kg. Considering a level of significance of 0.05 (5%), build a test of hypotheses to see whether the average lean body mass lost would be different between dieting and exercising for the population of men similar to the ones in this study.

a) Is this a one-sided or two-sided test?

b) Specify all four steps of your hypothesis test. Use the standard normal curve and Table 8.1 in Chapter 8 of the textbook to find an approximate p-value.

You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. How many randomly selected air passengers must you​ survey? Assume that you want to be 99​% confident that the sample percentage is within 2.5 percentage points of the true population percentage. Complete parts​ (a) and​ (b) below.

a. Assume that nothing is known about the percentage of passengers who prefer aisle seats.

___ (Round up to the nearest​ integer.)

b. Assume that a prior survey suggests that about 31​% of air passengers prefer an aisle seat.

___(Round up to the nearest​ integer.)

The heights of women follow an approximately normal distribution with a mean of 65 inches and a standard deviation of 3.5 inches. Use this information and a z-table to answer the following questions.

A. Bianca is 60 inches tall. Find the z-score for Bianca's height. Round your z-score to 2 decimal places.

B. Find the proportion of the population Bianca is taller than. Round your proportion to 4 decimal places.

C. What proportion of women are between 61.5 inches and 68.5 inches? Round your answer to four decimal places.

D. Fill in the blank. Round your answer to one decimal place. 25% of women are shorter than ______________ inches.

E. Fill in the blanks. Round your answers to one decimal place. The middle 60% of women have heights between _____________ inches and _______________ inches.

A random sample of 332 medical doctors showed that 176 had a solo practice.

(a) Let p represent the proportion of all medical doctors who have a solo practice. Find a point estimate for p. (Use 3 decimal places.)

(b) Find a 98% confidence interval for p. (Use 3 decimal places.)

What is the margin of error based on a 98% confidence interval? (Use 3 decimal places.)

1. T distribution with n degree of freedom is T=z/squart root (x/n) does that mean n-1 degree of freedom will be T=z/squart root (x/n-1) ?

2. what is the degrees of freedom. ????? please give me some examples

follow the comments please.

Waiters at a restaurant chain earn an average of $249 per shift (regular pay + tips) with a standard deviation of $39. For random samples of 36 shifts at the restaurant, within what range of dollar values will their sample mean earnings fall, with 95% probability?

Standard Normal Distribution Table

Range:

to

Round to the nearest cent

The mathematics department is considering revising how statistics is taught. In order to see if their changes will be effective in increasing student performance, they decided to run a Simulated Experiment. Previous semesters have that 10% of students receive an A in the class, 40% receive a B, and 20% receive a C. How would you assign values so you can use a Random Digit Table to run this experiment?

a) Assign 1 digit numbers as follows: 0 is A; 1, 2, 3, 4 are B; 5, 6 are C; 7, 8, 9 are D.

b) Assign 1 digit numbers as follows: 0 is A; 1, 2, 3, 4 are B; 5, 6 are C; 7, 8, 9 are other grades.

c) Assign 2 digit numbers as follows: 00-10 are A; 00-40 are B; 0-20 are C.

d) Assign 2-digit numbers as follows: 90-99 are A; 80-89 are B; 70-79 are C; 60-69 are D; and 00-59 are F.

e) This experiment cannot be simulated using a random digit table.

can you show steps using the TI-84 plus? not using excel function.

19. Mercury in Sushi An FDA guideline is that the mercury in fish should be below I part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in New York City. The study was sponsored by the New York Times, and the stores (in order) are D’Agostino, Eli’s Manhattan, Fairway, Food Emporium, Gourmet Garage, Grace’s Marketplace, and Whole Foods. Construct a 98% confidence interval estimate of the mean amount mercury in the population. Does it appear that there is too much mercury in tuna sushi?

0.56 0.75 0.10 0.95 1.25 0.54 0.88

-A random sample of 15 checking accounts at a bank showed an average balance of $280. The standard deviation of the sample was $60. Construct a 90% confidence interval for the mean and explain what it shows you in the context of the problem. Show your work and show your calcualtor steps.

-A local health center noted that in a sample of 400 patients 80 were referred to them by the local hospital. Provide a 95% confidence interval for the percentage of patients who were referred to the health center by the hospital and explain what it means in the context of the problem. Show your work and show your calcualtor steps.

The weights of the fish in a certain lake are normally distributed with a mean of 15.9 pounds and a standard deviation of 5.1 pounds. If 5 fish are randomly selected, find the probability that the mean weight is between 11.4 and 18.6 pounds. Round your answer 4 places after the decimal point.

In 2003, the Accreditation Council for Graduate Medical Education (ACGME) implemented new rules limiting work hours for all residents. A key component of these rules is that residents should work no more than 80 hours per week. The following is the number of weekly hours worked in 2017 by a sample of residents at the Tidelands Medical Center. 86 84 89 89 79 83 84 85 83 78 74 90

1. What is the point estimate of the population mean? (Round your answer to 2 decimal places.)

2. Develop a 90% confidence interval for the population mean. (Use t Distribution Table.) (Round your answers to 2 decimal places.)

3. Is the council's claim that the "typical resident" works 80 per month reasonable?

Question 7 (1 point)

Poker game: You pay $5 to play. A 7-card poker hand is dealt, and you are paid $89 if the hand contains a 3 of a kind [at least 3 cards of the same value] and nothing otherwise.

What is the expected value of your payoff from this game?

[Round to 3 digits after decimal point]

Your Answer:

3. Take the mean and standard deviation of data set A calculated in problem 1 and assume that they are population parameters (μ and σ) known for the variable fish length in a population of rainbow trouts in the Coldwater River. Imagine that data set B is a sample obtained from a different population in Red River (Chapter 6 problem!).

1. Conduct a hypothesis test to see if the mean fish length in the Red River population is different from the population in Coldwater River.
2. Conduct a hypothesis test to see if the variance in fish length is different in the Red River population compared to the variance in the Coldwater population.

Go into R and view all of the data sets preloaded in R by using the data() command. As you see there are quite a few data sets loaded into R. Now retrieve the dataset women using data(women). This data is from a random sample of 15 women, recording the height and weight of each woman in the sample. I want you to create a 95% confidence interval for the population mean using this data and R.

First find the sample mean using the mean() command and sample standard deviation using the sd() command. Now find t* using the qt() function. Look up help for this function to learn how to use it. Remember that for a 95% CI value, t* you want to find the value t for which P(T14 < t∗) = .975. Construct the margin of error using the R math functions. Now find the upper and lower ends of the confidence interval.

Now go to R help and look up the t.test function. Use the t.test to conduct the hypothesis testH0 : μ = 62.5 with Ha : μ ̸= 62.5. For this application, use women$height in place of x, mu=62.5 for the second argument, and alternative=“two.sided” for the third. Interpret the p-value in terms of your typical test sizes.

Does the null hypothesis value H0 : μ = 62.5 fall in the condfidence interval you constructed earlier? Now pick any value that falls inside the confidence interval you constructed. Conduct the t-test on that as the null value and report the p-value. Try other null values that fall inside your CI and conduct the t-test on these. What is the relationship between a 95% CI and a two-sided hypothesis test withα = .05?

In a sample of 331 Americans, 15% decided to not go to college do so because they cannot afford it.

(a) Suppose we wanted the margin of error for the 90% confidence level to be at most 1.5%. How large of a survey would you recommend? (Do not use the estimate of p given by the sample.)

(b) Suppose we wanted the margin of error for the 90% confidence level to be at most 1.5%. How large of a survey would you recommend? (Now make the estimate that p≈0.15 .)