An article in Fortune magazine reported on the rapid rise of fees and expenses charged by mutual funds. Assuming that stock fund expenses and municipal bond fund expenses are each approximately normally distributed, suppose a random sample of 12 stock funds gives a mean annual expense of 1.63 percent with a standard deviation of 0.45 percent, and an independent random sample of 12 municipal bond funds gives a mean annual expense of 0.93 percent with a standard deviation of 0.20 percent. Let µ₁ be the mean annual expense for stock funds, and let µ₂ be the mean annual expense for municipal bond funds. Do parts a, b, and c by using the equal variances procedure.

(a) Set up the null and alternative hypotheses needed to attempt to establish that the mean annual expense for stock funds is larger than the mean annual expense for municipal bond funds. Test these hypotheses at the 0.05 level of significance. (Round your s_p² answer to 4 decimal places and t-value to 2 decimal places.)

H0: µ_1-µ_{2 <\= _____ versus Ha: ____ _____
s2p = _________ t= _________
(reject/do not reject) H0 with a = 0.05}

(b) Set up the null and alternative hypotheses needed to attempt to establish that the mean annual expense for stock funds exceeds the mean annual expense for municipal bond funds by more than 0.5 percent. Test these hypotheses at the 0.05 level of significance. (Round your t-value to 2 decimal places and other answers to 1 decimal place.)

H0: µ_1-µ_{2 _____ _______ versus Ha:} µ_1-µ_{2 ____ _______
t= _________
(reject/do not reject) H0 with a = 0.05}

(c) Calculate a 95 percent confidence interval for the difference between the mean annual expenses for stock funds and municipal bond funds. Can we be 95 percent confident that the mean annual expense for stock funds exceeds that for municipal bond funds by more than .5 percent? (Round your answers to 3 decimal places.)

The interval = [_____, _____] (Yes/No), the interval is (above/below) 0.05.

A magazine collects data each year on the price of a hamburger in a certain fast food restaurant in various countries around the world. The price of this hamburger for a sample of restaurants in Europe in January resulted in the following hamburger prices (after conversion to U.S. dollars).

The mean price of this hamburger in the U.S. in January was $4.62. For purposes of this exercise, assume it is reasonable to regard the sample as representative of these European restaurants. Does the sample provide convincing evidence that the mean January price of this hamburger in Europe is greater than the reported U.S. price? Test the relevant hypotheses using

α = 0.05.

(Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

State your conclusion.

Reject H₀. We have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.62.Do not reject H₀. We do not have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.62.    Do not reject H₀. We have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.62.Reject H₀. We do not have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.62.

Find an article in a newspaper or magazine (or the online equivalent) describing a recent study in which the researchers collected data through observation or an experiment to draw a conclusion. A simple poll (like “43% of Americans like to eat sushi”) is not sufficient; you should be looking for something describing a significant research study. Some examples (don’t limit yourself to these): an experiment testing a new drug or medical procedure a study linking a food or exercise with causing or reducing the risk of a disease a study about how some new teaching approach improves learning a study about how people behave (example: a study showing incentives can cause us to be less efficient)

"Readability Levels of Magazine Ads," by F.K. Shuptrine and D.D. McVicker, is an article in the Journal of Advertising Research. The following is a list of the number of three-syllable (or longer) words in advertising copy of randomly selected magazine advertisements. 34 21 37 31 10 24 39 10 17 18 32 17 3 10 6 5 6 6 13 22 25 3 5 2 9 3 0 4 29 26 5 5 24 15 3 8 16 9 10 3 12 10 10 10 11 12 13 1 9 43 13 14 32 24 15 Use eight classes

. (a) Find the class width.

(b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Round your relative frequencies to two decimal places.) Class Limits Class Boundaries Lower − Upper Lower − Upper Midpoint Frequency Relative Frequency Cumulative Frequency 0 − 5 − 6 − 11 − 12 − 17 − 18 − 23 − 24 − 29 − 30 − 35 − 36 − 41 − 42 − 47 −

(c) Draw a histogram. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot

(d) Draw a relative-frequency histogram. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (e) Categorize the basic distribution shape. uniform skewed right bimodal skewed left mound-shaped symmetrical

1. In an article about the cost of health care, Money magazine reported that a visit to a hospital emergency room for something as simple as a sore throat has a mean cost of $328 (Money, January 2009). Assume that the cost for this type of hospital emergency room visit is normally distributed with a standard deviation of $92. Answer the following questions about the cost of a hospital emergency room visit for this medical service.

1. What is the probability that the cost will be more than $500?

2. What is the probability that the cost will be less than $250?

3. What is the probability that the cost will be between $300 and $400?

4. If the cost to a patient is in the lower 8% of charges the cost of this patient’s emergency room visits?

A magazine claims that the mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry World. The results for the samples of customer transactions for the two fast food restaurants are given below. At the α =0.01, can you support the magazine’s claim? Assume the population variances are equal

Burger Stop x1= $5.46 s1= $0.89 n1= 22

Fry World x2=$5.12 s2=$0.79 n2=30

3. An advertising firm wants to determine the effects of the color of a magazine advertisement on the response of magazine readers. A random sample of readers is shown ads of four different colors, (Blue, Green, Yellow, Red) and three different sizes, (Small, Medium, Large.) The readers were asked to rate the ads from 1 to 12. The advertising firm felt that the size of the ad might make a difference, so they made sure that each color had an equal chance to be matched with each ad size. They weren’t so interested in the ad size; they just didn’t want the ad size to mask any differences due to the ad color.

Color: Blue,Blue,Blue,Green,Green,Green,Yellow,Yellow,Yellow,Red,Red,Red

Size: Small,Medium,Large, Small,Medium,Large, Small,Medium,Large, Small,Medium,Large

Rating: 2,3,5,3,5,6,3,6,7,8,9,12

Use a 5% significance level, α=0.05 for all hypothesis tests and confidence intervals. Conduct the appropriate analysis.

3.1 In your own words state the null and alternative hypothesis statements for the factor of interest.

3.2 What can we conclude about the factor of interest?

3.3 If appropriate, create Tukey simultaneous 95 percent confidence intervals and make pairwise comparisons if appropriate. If not appropriate, state why we would not make pairwise comparisons.

1. As reported in Runners World magazine, the times of the finishers in the New York City 10 km run follow the normal model with mean=61 minutes and standard deviation= 9 minutes.

a) Using the 68-95-99.7% rule, 68% of runners will finsh between which two times? (In minutes)

b) Using the 68-95-99.7% rule, 99.7% of runners will finish between which two times? (In minutes)

Use z-scores and your z-table for the following. Round z-scores to two decimal places but give the full decimal answer from the z-table.

c) What proportion of runners will finish in less than 49.75 minutes?

d) What proportion of runners will take more than 65 minutes to finish?

e) For a random runner of the 10 km run, what is the probability they will finish between 55 and 70 minutes?

f) What time in (in minutes) will 30% of all runners finish below?

g) What time (in minutes) will 10% of the runners finish above?