***PLEASE TYPE ANSWERS***

Five students were tested before and after taking a class to improve their study habits. They were given articles to read which contained a known number of facts in each story. After the story each student listed as many facts as he/she could recall. The following data was recorded.

On the planet of Mercury, 4-year-olds average 3 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.4 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose Mercury News) Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)  

b. Find the probability that the child spends less than 3.1 hours per day unsupervised.  

c. What percent of the children spend over 2.2 hours per day unsupervised. % (Round to 2 decimal places)

d. 84% of all children spend at least how many hours per day unsupervised?  hours.

In the US, 44.3% of all people have type O blood, 41% have type A blood, 10.2% have type B blood and 4.5% have type AB blood. A researcher wants to see if the distribution of blood type is different for millionaires. The table below shows the results of a random sample of 2864 millionaires. What can be concluded at the αα = 0.01 significance level?

Complete the table by filling in the expected frequencies. Round to the nearest whole number:
Frequencies of Blood Type

OutcomeFrequencyExpected Frequency

O1258

A1181

B281

AB144

What is the correct statistical test to use?
Select an answer Independence Goodness-of-Fit Homogeneity Paired t-test

What are the null and alternative hypotheses?
H0:H0:

Blood type and income are dependent.

The distribution of blood type for millionaires is not the same as it is for Americans in general.

Blood type and income are independent.

The distribution of blood type for millionaires is the same as it is for Americans in general.

H1:H1:

The distribution of blood type for millionaires is not the same as it is for Americans in general.

Blood type and income are independent.

Blood type and income are dependent.

The distribution of blood type for millionaires is the same as it is for Americans in general.

The degrees of freedom =

The test-statistic for this data =  (Please show your answer to three decimal places.)

The p-value for this sample = (Please show your answer to four decimal places.)

The p-value is Select an answer greater than less than (or equal to)  αα

Based on this, we should Select an answer accept the null fail to reject the null reject the null

Thus, the final conclusion is...

There is insufficient evidence to conclude that blood type and income are dependent.

There is sufficient evidence to conclude that the distribution of blood type for millionaires is the same as it is for Americans in general.

There is insufficient evidence to conclude that the distribution of blood type for millionaires is not the same as it is for Americans in general.

There is sufficient evidence to conclude that the distribution of blood type for millionaires is not the same as it is for Americans in general.

There is sufficient evidence to conclude that blood type and income are dependent.

Johnson has recently opened his workshop at the main street of a major city in the North East. Johnson estimates about 20 cars arriving at his workshop for repairs every day. Based on industry data, he estimates that 40% of the arrivals will agree to have the work repaired at his workshop. His average daily cost at the workshop is $1200. He expects to make a revenue of $200 for each car that is repaired. Johnson would like to know the following information: a) The probability that no car will arrive at his workshop for repair on a given day. b) The probability that he will have at least 4 cars to repair on a given day. c) The expected daily profit assuming that he is able to repair all the arriving cars in a day. d) Develop a probability distribution for this problem.

An employee of a small software company in Minneapolis bikes to work during the summer months. He can travel to work using one of three routes and wonders whether the average commute times (in minutes) differ between the three routes. He obtains the following data after traveling each route for one week.

a-1. Construct an ANOVA table. (Round "Sum Sq" to 1 decimal place, "Mean Sq" and "F value" to 2, and round the "p-value" to 4 decimal places.)

ANOVA

a-2. At the 5% significance level, do the average commute times differ significantly between the three routes. Assume that commute times are normally distributed.

• Yes, since the p-value is less than significance level.

• Yes, since the p-value is not less than significance level.

• No, since the p-value is less than significance level.

• No, since the p-value is not less than significance level.

b. Use Tukey’s HSD method at the 5% significance level to determine which routes' average times differ. (Round difference to 1 decimal place, confidence interval bounds to 2 decimal places, and p-values to 3.)

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.† Over a period of months, an adult male patient has taken seven blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.77 mg/dl.

(a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is known n is large normal distribution of uric acid σ is unknown uniform distribution of uric acid

(c) Give a brief interpretation of your results in the context of this problem.

There is not enough information to make an interpretation.

The probability that this interval contains the true average uric acid level for this patient is 0.05.   

The probability that this interval contains the true average uric acid level for this patient is 0.95.

There is a 5% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.

There is a 95% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.

(d) Find the sample size necessary for a 95% confidence level with maximal error of estimate E = 1.08 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)
blood tests

1. A researcher wants to know if the typing speed of a secretary in words per minute is related to the time in hours that it takes to learn the new word processing program. Below is speed versus hours to learn program. What is the regression equation? Typing speed --48- 74 - 52-- 79-- 83-- 56-- 85-- 63-- 88-- 74-- 90-- 92 Time hrs.----- --7---- 4---- 8 -- 3.5 --2 -- 6 ---2.3-- 5 -- 2.1-- 4.5--1.9- 1.5 Select one: a. y = 0.19 x - 18.7 b. y = 0.354 x - 21.3 c. y= -0.137 X + 14.086 d. y = 0.34 X - 19.8

2. A researcher wants to know if the typing speed of a secretary in words per minute is related to the time in hours that it takes to learn the new word processing program. Below is speed versus hours to learn program. Find the 90 % prediction interval for number of hours it would take an average secretary who has a typing speed of 72 words per minute to learn the word processing program.

Typing speed --48- 74 - 52- 79-- 83- 56- 85- 63- 88- 74- 90- 92
Time hrs.----- --7- ---4--- 8 - 3.5----2 - 6 --2.3- 5 - 2.1- 4.5-1.9- 1.5

Select one:

a. 2.5 < y < 5.4

b. 3.34 < y < 5.1

c. 4.5 < y < 6.25

d. 2.5 < y < 4.8

3. A researcher wants to know if the typing speed of a secretary in words per minute is related to the time in hours that it takes to learn the new word processing program. Below is speed versus hours to learn program. What is the correlation coefficient?

Typing speed --48- 74 - 52- 79-- 83- 56- 85- 63- 88- 74- 90- 92
Time hrs.----- --7- ---4--- 8 - 3.5----2 - 6 --2.3- 5 - 2.1- 4.5-1.9- 1.5

4. A researcher wants to know the relationship between the number of cows ( in thousands) in certain counties and the milk production ( in million pounds).
The data is shown below. Estimate the amount of milk if there are 125 million cows in the county. Write answer in millions of pounds (85 if there are 85 million pounds)

Cows (millions) ------70-----3-----194-----12-----46-----65
Milk (Million #)--------115----5-----289-----15-----72-----92

5.

Question text

A researcher wants to know if the typing speed of a secretary in words per minute is related to the time in hours that it takes to learn the new word processing program. Below is speed versus hours to learn program. Predict the number of hours it would take an average secretary who has a typing speed of 72 words per minute to learn the word processing program.

Typing speed --48- 74 - 52- 79-- 83- 56- 85- 63- 88- 74- 90- 92
Time hrs.----- --7- ---4--- 8 - 3.5----2 - 6 --2.3- 5 - 2.1- 4.5-1.9- 1.5

6.

Question text

A researcher wants to know if the typing speed of a secretary in words per minute is related to the time in hours that it takes to learn the new word processing program. Below is speed versus hours to learn program. Find the standard error of estimate for an average secretary who has a typing speed of 72 words per minute to learn the word processing program.

Typing speed --48- 74 - 52- 79-- 83- 56- 85- 63- 88- 74- 90- 92
Time hrs.----- --7- ---4--- 8 - 3.5----2 - 6 --2.3- 5 - 2.1- 4.5-1.9- 1.5

Suppose x has a distribution with μ = 10 and σ = 3.

(a) If a random sample of size n = 47 is drawn, find μx, σ x and P(10 ≤ x ≤ 12). (Round σx to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(10 ≤ x ≤ 12) =

(b) If a random sample of size n = 58 is drawn, find μx, σ x and P(10 ≤ x ≤ 12). (Round σ x to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(10 ≤ x ≤ 12) =

(c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).) The standard deviation of part (b) is part (a) because of the sample size. Therefore, the distribution about μx is

Two different rifles are tested at the shooting range. Rifle one was fired 190 times and the target hit 158 times. Rifle two was shot 140 times and the target hit 107 times. Use α = 0.05 for the following.

a. Is it reasonable to conclude the rifles are equally accurate? Provide the hypothesis tested, the rejection region employed, the statistic calculated, the p-value and the conclusion reached.

b.   Provide the 95% confidence interval on the difference between the two proportion of targets hit.

An elevator has a placard stating that the maximum capacity is 1304 lb long dash—88 passengers.​ So, 88 adult male passengers can have a mean weight of up to 1304 divided by 8 equals 163 pounds.1304/8=163 pounds. If the elevator is loaded with 88 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 163 lb.​ (Assume that weights of males are normally distributed with a mean of 170  lb and a standard deviation of 32 lb​.) Does this elevator appear to be​ safe?

Duke Energy reported that the cost of electricity for an efficient home in a particular neighborhood of Cincinnati, Ohio was $107 per month. A researcher believes that the cost of electricity for a comparable neighborhood in Chicago, Illinois is higher. A sample of homes in this Chicago neighborhood will be taken and the sample mean monthly cost of electricity will be used to test the following null and alternative hypotheses. H0: μ ≤ 107 Ha: μ > 107 a. Assume the sample data lead to rejection of the null hypothesis. What would be your conclusion about the cost of electricity in the Chicago neighborhood? b. What is the Type I error in this situation? The Type I error is H0 when it is . What are the consequences of making this error? c. What is the Type II error in this situation? The Type II error is H0 when it is . What are the consequences of making this error

8. For each of the following, identify the distribution based on the MGF. Be sure to specify name of distribution and value(s) of parameter(s).

(a) MX(t) = (0.3 + 0.7 e t ) 9 , t ∈ (−∞,∞).

(b) MX(t) = 0.8 e t + 0.2, t ∈ (−∞,∞).

(c) MX(t) = e 9(e t−1), t ∈ (−∞,∞).

(d) MX(t) = 0.75e t 1−0.25e t , t < − ln 0.25.

(e) MX(t) = 0.4e t 1−0.6e t 20, t < − ln 0.6.

The manager of a travel agency asked you to come up with a forecasting technique that will best fit to the actual demand for packaged tours. You have observed and recorded the actual demand for the last 10 periods. You also identified two possible techniques for consideration: 2-month moving averages (F1), and exponential smoothing (F2) with a smoothing constant of 0.40. Using Cumulative Forecasting Error (CFE) and Mean Absolute Deviation (MAD) as your performance measures you will determine the technique that will best fit to the actual demand data provided in the following table.
  
STEP 1: Given start forecast values in period 3, compute forecast values from period 4 to 10. You are asked to provide the forecast values for period 6 and 10 for both techniques.

  
  
STEP 2: Using data from period 3 to period 10,
  
Provide the performance measures for F1 technique:
  
            CFE =                         MAD =  
  
Provide the performance measures for F2 technique:
  
            CFE =             MAD =  
  
Based on these measures, which technique best fit to your data? (Enter F1 or F2) =  
NOTE: All computed forecast values should be rounded to the nearest integer (no decimal, for example 190). Performance measures (CFE and MAD) must be rounded to the nearest hundredth (two decimals after the dot, for example 30.99).
  
  

1)A professor using an open-source introductory statistics book predicts that 60% of the students will purchase a hard copy of the book, 25% will print it out from the web, and 15% will read it online. She has 200 students this semester. Assuming that the professor's predictions were correct, calculate the expected number of students who read the book online.

2)The number of AIDS cases reported for Santa Clara County, California is broken down by race in the table below. Source: "HIV/AIDS Epidemiology Santa Clara County", Santa Clara County Public Health Department, May 2011.

Directions: Conduct a chi-square test for goodness-of-fit to determine whether or not the occurrence of AIDS cases is consistent with the race distribution of Santa Clara County.

1. Choose the correct null and alternative hypotheses.
   • H0:H0: The distribution of AIDS cases is consistent with the race distribution in Santa Clara County.
     HaHa The distribution of AIDS cases is different from the race distribution in Santa Clara County.
   • H0H0 The distribution of AIDS cases is different from the race distribution in Santa Clara County.
     Ha:Ha: The distribution of AIDS cases is consistent with the race distribution in Santa Clara County.
2. Compute the test statistic.
   
   The population distribution of Santa Clara County by race is provided in the table below. Use these percentages to compute the expected number of cases for each racial group. Round each of the expected counts to 2 decimal places.
   

   Race	Proportion	Expected cases
   White	0.424
   Hispanic	0.259
   Black	0.025
   Asian/Pacific Islander	0.292
   Total	1

   
   Determine the value of the test statistic. Round your answer to 1 decimal place.
   
   χ2=χ2=
   
3. Compute the p-value. Round your answer to 4 decimal places.
   
   p-value =
   
4. Interpret the results of the significance test.
   • The differences between the distribution of AIDS cases and the distribution of the general population in Santa Clara County are not statistically significant. From a practical perspective, the differences are minor.
   • The differences between the distribution of AIDS cases and the distribution of the general population in Santa Clara County is statistically significant. The differences are also important from a practical perspective. For example, the number of blacks with AIDS is 3.6 times more than expected and the number of Asian/Pacific Islanders with AIDS is 4.1 times less than expected.

Please answer the following questions based on the given graph

(1) Create a Time Series (Trend)Model  for  passengers on Domestic flights. (To zero decimal places) The predicted amount of passengers for 2010 on Domestic flights is ________.

(2) Create a Time Series (Trend)Model  for  passengers on Domestic flights. (To zero decimal places) On average, the number of passengers of domestic flights increase by ________each year, keeping all else equal.

(3)Create a GrowthModel  for  passengers on Domestic flights. (To zero decimal places) The predicted amount of passengers for 2010 on Domestic flights is ________.

(4)Create a Growth Model  for passengers on Domestic flights. (To two decimal places) On average, the number of passengers of domestic flights increase by ________percent each year, keeping all else equal.

(5) Based on R-squared which model is better for predicting passengers of domestic flights?
Time Series (Trend) Model
Growth Model