1. People claim that women say more words per day than men. Estimates claim that a woman uses roughly 20,000 words per day, while a man uses approximately 7,000. To investigate this, a researcher recorded conversations of male college students over a 5-day period. The results are as follows:

The researcher believes that many use more than 7,000 words per day.

1. State the problem in your own words.
2. Create a plan for testing the researcher’s claim. Be sure to state the null and alternate hypotheses.
3. Carry out the appropriate hypothesis test. Begin by finding the sample mean and standard deviation. Give the value of the t statistic and give the p-value (or an estimate).
4. Formulate the statistical conclusion in terms of the null hypothesis and a practical conclusion. You may compare the p-value to 0.05 to determine if the null hypothesis should be rejected. When the p-value is less than 0.05, we reject the null hypothesis. Otherwise, we fail to reject the null.

Many high school students take the SAT's twice; once in their Junior year and once in their Senior year. The Senior year scores (x) and associated Junior year scores (y) are given in the table below. This came from a random sample of 35 students. Use this data to test the claim that retaking the SAT increases the score on average by more than 25 points. Test this claim at the 0.10 significance level.

Are all colors equally likely for Milk Chocolate M&M's? Data collected from a bag of Milk Chocolate M&M's are provided.

Blue            Brown        Green          Orange       Red          Yellow

110                   47               52                 103            58                50

a. State the null and alternative hypotheses for testing if the colors are not all equally likely for Milk Chocolate M&M's.

b. If all colors are equally likely, how many candies of each color (in a bag of 420 candies) would we expect to see?

c. Is a chi-square test appropriate in this situation? Explain briefly.

d. How many degrees of freedom are there?

A) 2 B) 3 C) 4 D) 5

e. Calculate the chi-square test statistic. Report your answer with three decimal places.

f. Report the p-value for your test. What conclusion can be made about the color distribution for Milk Chocolate M&M's? Use a 5% significance level.

g. Which color contributes the most to the chi-square test statistic? For this color, is the observed count smaller or larger than the expected count?

Assume that a sample is used to estimate a population proportion p. Find the 99.9% confidence interval for a sample of size 199 with 121 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.

99.9% C.I. =

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

The proportion of adult women in a certain geographical region is approximately 51​%. A marketing survey telephones 400 people at random. Complete parts a through e below.

How would the confidence interval change if the confidence level had been 90​% instead of 98​%?

Situation: The Ipod Touch has been out for two years now and a lot of data has been collected.

Relevant Relationship:
There is a functional relationship between Price of an IPod Touch,pp and Weekly Demand,ss.
Below is a table of data that have been collected

A.. Find the linear model that best fits this data using regression and enter the model below
(for entry round the linear parameter value to nearest 0.01 and constant parameter to nearest 1)
s=T(p)=s=T(p)=   

Now answer these two questions using the UNROUNDED model parameters


B. What does the model predict will be the weekly demand if the price of an ipod touch is $249 ?  (nearest 100)

C. According to the model at what should the price be set in order to have a weekly demand of 189,600 ipod Touches? $ (nearest $1)

Let X1, X2, X3, X4, X5 be independent continuous random variables having a common cdf F and pdf f, and set p=P(X1 <X2 <X3 < X4 < X5).

(i) Show that p does not depend on F. Hint: Write I as a five-dimensional integral and make the change of variables ui = F(xi), i = 1,··· ,5.

(ii) Evaluate p.
(iii) Give an intuitive explanation for your answer to (ii).

(Similar to Ghahramani Section 3.4, Problems 6, 8, and 14) Three black boxes are labeled with Roman numerals I, II and III.

• Box I contains four red chips and three blue chips.

• Box II contains two red chips and five blue chips.

• Box III contains seven red chips and no blue chips. Solve each of the following problems.

(a) Suppose a box is selected at random and three chips are drawn at random from the box. If all three chips are red, what is the probability they were drawn from Box I?

(b) Suppose one chip is selected at random from each box. If two of the three chips drawn are red chips, what is the probability that the chip drawn from Box II was red?

(c) Suppose three chips are randomly selected from Box I and placed in Box III. If a chip subsequently drawn randomly from Box III is blue, what is the probability that all three chips moved from Box I to Box III were blue.

Julia enjoys jogging. She has been jogging over a period of several years, during which time her physical condition has remained constantly good. Usually she jogs 2 miles per day. During the past year Julia recorded how long it took her to run 2 miles. She has a random sample of 95 of these times. For these 95 times the mean was 15.60 minutes and the standard deviation s=1.80 minutes. Find the margin of error (round to 2 decimal places) and the 90% confidence interval for Julia’s average running time.

Colorado voted recently on legalizing recreational marijuana use. Prior to the election,

pollsters working in favor of legalization wanted to estimate the proportion of California

voters that were in favor of the proposed law. The pollsters wanted a margin of error of 0.01 and a confidence level of 95% for their estimate.

1. What sample size did they need? (Assume p* or  = 0.5.)
2. The pollsters’ budget was not big enough to accommodate a sample of that size. So, instead, they decided to go for a margin of error of 0.05. What sample size do they need? (Again, assume p* or  = 0.5.)

The processing time for the shipping of packages for a company, during the holidays, were recorded for 48 different orders. The mean of the 48 orders is 10.5 days and the standard deviation is 3.08 days. Raw data is given below. Use a 0.05 significance level to test the claim that the mean package processing time is less than 12.0 days. Is the company justified in stating that package processing is completed in under 12 days?

1) Write Ho (null) and H1 (alternative) and indicate which is being tested

2) Perform the statistical test and state your findings; Write answer as a statement

1. In preparing to do a study on the proportion of people who use internet gambling sites, you must determine how

many people to survey. If you want to be 99% confident that the population proportion is within 3 percentage

points, how many people must you survey?

2.The National Health and Nutrition Examination Survey reported that in a recent year, the mean serum cholesterol

level for U.S. adults was 202, with a standard deviation of 41 milligrams per deciliter. A simple random sample of

110 adults is choose, find the probability that the mean cholesterol level is greater than 210.

3. In a Gallup poll, 64% of the people polled answered yes to the following question: “Are you in favor of

the death penalty for a person convicted of murder?” The margin of error in the poll was 3% and the

estimate was made with 90% confidence. At least how

many people were surveyed?

Closer to the November election, better precision and smaller margins of error are desired. Assume the following margins of error are requested for surveys to be conducted during the electoral campaign. Assume a planning value of p^* = 0.50 and a 90% confidence level. What is the recommended sample size for each survey? Show work

1. For September, the desired margin of error is 0.045. ____________

2. For October, the desired margin of error is 0.035. ____________

3. For early November, the desired margin of error is 0.025. ____________

4. For pre-election day, the desired margin of error is 0.015. ____________

A survey of 24 randomly sampled judges employed by the state of Florida found that they earned an average wage (including benefits) of $57.00 per hour. The sample standard deviation was $6.02 per hour. (Use t Distribution Table.)

1. What is the best estimate of the population mean?

2. Develop a 98% confidence interval for the population mean wage (including benefits) for these employees. (Round your answers to 2 decimal places.)