5. Describe what we know about the theoretical distribution of sample means. Be sure to
include answers to the questions that follow:
What is a distribution of sample means? How is this different from the
distributions we have been working with up through Chapter 6?
According to the Central Limit Theorem, what three things do we know about
the theoretical distribution of sample means?
Define standard error.
In your own words, what does standard error tell us and why do we need this
information?
How is standard error different from standard deviation?
In: Math
A facility has a waste storage tank with a capacity of 40 cubic feet. Each week the tank produces either 0, 10, 20, or 30 cubic feet of waste with respective probabilities of 0.1, 0.4, 0.3, and 0.2. If the amount of waste produced in a week creates a situation where the tank would overflow, the amount exceeding the tank’s capacity can be removed at a cost of $3 per cubic foot. At the end of each week, a contracted service is available to remove waste. The service costs $40 for each visit plus $1 per cubic foot of waste removed. The facility manager decides to adopt a policy where, if the tank contains more than 20 cubic feet of waste, the contract service comes at the end of the week and removes all of the waste in the tank. Otherwise, the service does not come, and no waste is removed. Model the amount of waste in the tank as a Markov chain. Pay particular attention to when (at what point in the week) the amount of waste is measured or recorded
In: Math
A study was done to explore the number of chocolate bars consumed by 16-year-old girls in a month's time. The results are shown below. Number of Chocolate Bars Consumed 56 46 12 62 39 24 59 51 39 52 28 41 10 64 27 0 34 5 55 32 42 24 14 63 1 63 52 58 52 26 Use the data from the chocolate bar study to answer the following questions. Use SPSS for all calculations. Copy and paste the SPSS output into the word document, highlighting the correct answer. Additionally, type the correct answer into your word document next to the corresponding question. 1. Identify the level of measurement used in this study. 2. Using SPSS, run descriptive statistics on the data: a. Find the mean, median, and mode of the number of chocolate bars consumed by 16-year-old girls in a month. b. Find the variance and standard deviation of the number of chocolate bars consumed by 16-year-old girls in a month. 3. Create a frequency distribution table with six intervals/classes. 4. Create a histogram based on the Frequency table in problem 3.
In: Math
An ANOVA table for a one-way experiment gives the following:
Source df SS
Between factors 2 810
Within (error) 8 720
Answer true or false and explain for the following six statements:
The null hypothesis is that all four means are equal.
The calculated value of F is 4.500.
The critical value for F for 5% significance is 6.06.
The null hypothesis cannot be rejected at 5% significance.
The null hypothesis cannot be rejected at 1% significance.
There are 10 observations in the experiment.
In: Math
7.20 Body measurements, Part III. Exercise 7.13 introduces data on shoulder girth and height of a group of individuals. The mean shoulder girth is 107.30 cm with a standard deviation of 10.34 cm. The mean height is 171.14 cm with a standard deviation of 9.41 cm. The correlation between height and shoulder girth is 0.69. 1. (a) Write the equation of the regression line for predicting height. 2. (b) Interpret the slope and the intercept in this context. 3. (c) Calculate R2 of the regression line for predicting height from shoulder girth, and interpret it in the context of the application. 4. (d) A randomly selected student from your class has a shoulder girth of 100 cm. Predict the height of this student using the model. 5. (e) The student from part (d) is 160 cm tall. Calculate the residual, and explain what this residual means. 6. (f) A one year old has a shoulder girth of 56 cm. Would it be appropriate to use this linear model to predict the height of this child? *answers to 3 decimal points*!!!
In: Math
Roll two ordinary dice and let X be their sum. Draw the pmf and cmf for X. Compute the mean and standard deviation of X. Solve using R studio coding.
In: Math
Suppose there is a basket containing one apple and two oranges. A student randomly pick one fruit from the basket until the first time the apple is picked. (Sampling with replacement)
(a) What is the sample space for this experiment? What is the probability that the student pick the apple after i tosses?
(b) What is the expected number of times the students need to pick the apple?
(c) Let E be the event that the first time an apple is picked up is after an even number of picks. What set of outcomes belong to this event? What is the probability that E occurs?
In: Math
Your friend texted you a question. You did some research and found that a Minifig is a package containing one figurine. You also found out that, for every 60 packs produced, 4 of those are Chip and 4 are Dale.
A) What is the probability of opening one box and getting Chip?
B) What is the probability of opening one box and getting Chip OR Dale?
C) What is the probability of opening two boxes and specifically getting Chip in the first box and Dale in the second box?
D) What is the probability of opening two boxes and getting one Chip and one Dale (in either order)?
ANSWER ALL PARTS A-D
In: Math
In a certain population, 25% of the person smoke and 7% have a certain type of heart disease. Moreover, 10% of the persons who smoke have the disease.
What percentage of the population smoke and have the disease?
What percentage of the population with the disease also smoke?
In: Math
1. Assume that a sample is used to estimate a population
proportion p. Find the 90% confidence interval for a
sample of size 112 with 28% successes. Enter your answer as a
tri-linear inequality using decimals (not percents) accurate to
three decimal places.
2. You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 88%. You would like to be 98% confident that your estimate is within 3% of the true population proportion. How large of a sample size is required? n= ________
3. You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=43.7σ=43.7. You would like to be 90% confident that your estimate is within 3 of the true population mean. How large of a sample size is required? n= _____
In: Math
An investor holding a certain portfolio consisting of two stocks invests 20% in Stock A and 80% in Stock B. The expected return from Stock A is 4% and that from Stock B is 12%. The standard deviations are 8% and 10% for Stocks A and B respectively. Compute the expected return of the portfolio. b) Compute the standard deviation of the portfolio assuming the correlation between the two stocks is 0.75. c) Compute the standard deviation of the portfolio assuming the correlation between the two stocks is 1. d) Compare your answers in (b) and (c). What do you observe and why?
In: Math
From public records, individuals were identified as having been charged with drunken driving not less than 6 months or more than 12 months from the starting date of the study. Two random samples from this group were studied. In the first sample of 29 individuals, the respondents were asked in a face-to-face interview if they had been charged with drunken driving in the last 12 months. Of these 29 people interviewed face to face, 11 answered the question accurately. The second random sample consisted of 43 people who had been charged with drunken driving. During a telephone interview, 28 of these responded accurately to the question asking if they had been charged with drunken driving during the past 12 months. Assume the samples are representative of all people recently charged with drunken driving. Please show all steps in getting the answer.
(a) Categorize the problem below according to parameter being estimated, proportion p, mean μ, difference of means μ1 – μ2, or difference of proportions p1 – p2. Then solve the problem.
μ
μ1 – μ2
p
p1 – p2
(b) Let p1 represent the population proportion of all people with recent charges of drunken driving who respond accurately to a face-to-face interview asking if they have been charged with drunken driving during the past 12 months. Let p2 represent the population proportion of all people who respond accurately to the question when it is asked in a telephone interview. Find a 95% confidence interval for p1 – p2. (Use 3 decimal places.)
lower limit
upper limit
(c) Does the interval found in part (a) contain numbers that are all positive? all negative? mixed? Comment on the meaning of the confidence interval in the context of this problem. At the 95% level, do you detect any differences in the proportion of accurate responses to the question from face-to- face interviews as compared with the proportion of accurate responses from telephone interviews?
Because the interval contains only positive numbers, we can say that there is a higher proportion of accurate responses in face-to-face interviews.
Because the interval contains both positive and negative numbers, we can not say that there is a higher proportion of accurate responses in face-to-face interviews.
We can not make any conclusions using this confidence interval.
Because the interval contains only negative numbers, we can say that there is a higher proportion of accurate responses in telephone interviews.
In: Math
(1) A researcher wants to test H0: x1 = x2 versus the two-sided alternative Ha: x1 ≠ x2.
(a) This alternative hypothesis indicates a one-sided hypothesis instead of a two-sided hypothesis.
(b) The alternative hypothesis Ha should indicate that x1 ≥ x2 .
(c)The null hypothesis (but not the alternative hypothesis) should involve μ1 and μ2 (population means) rather than x1 and x2 (sample means).
(d) Hypotheses should involve μ1 and μ2 (population means) rather than x1 and x2 (sample means).
(e) The null hypothesis H0 should indicate that the two means are not equal.
(2) A study recorded the IQ scores of 50 college freshmen. The scores of the 24 males in the study were compared with the scores of all 50 freshmen using the two-sample methods of this section.
(a)The samples are too large to be used for hypothesis testing.
(b)The samples are not independent; we would need to compare the 24 males to the 26 females.
(c) The samples are too small to be used for hypothesis testing.
(d)The sample sizes are too different to be used for hypothesis testing; we would need to have more males in the sample.
(e)A two-sample method is not appropriate in this situation.
(3)A two-sample t statistic gave a P-value of 0.93. From this we can reject the null hypothesis with 90% confidence.
(a)We can reject the null hypothesis, but with less than 90% confidence.
(b) We need the P-value to be small to reject H0.
(c) We can reject the null hypothesis, but with more than 90% confidence.
(d) We need the P-value to be negative to reject H0.
(e)A P-value of this size is impossible.
(4)A researcher is interested in testing the one-sided alternative Ha: μ1 < μ2. The significance test gave t = 2.25. Since the P-value for the two-sided alternative is 0.04, he concluded that his P-value was 0.02.
(a) The alternative hypothesis should state that Ha: μ1 ≠ μ2.
(b) A one-sided alternative should never be used.
(c) The alternative hypothesis should state that Ha: μ1 ≤ μ2.
(d) Assuming the researcher computed the t statistic using x1 − x2,a positive value of t does not support Ha.
(e)A t statistic of this size should have a much larger P-value associated with it.
In: Math
Solve this word problem using step by step procedure: The math department at a local university has customarily advised students to purchase Calculator A. The manufacturer has recently released a new model, Calculator B, which is reputed to be more user-friendly. The faculty decided to determine if there is a difference in the time required to perform a certain common statistical calculation. Twelve students chosen at random are given drills with both calculators so that they are familiar with the operation of each type. Then the time they take to complete the test calculation on each device is measured in seconds (which calculator they are to use first is determined by some random procedure to control for any additional learning during the first calculations). To be clear, each student worked through a particular type of statistics problem with one calculator and then did a similar problem on the other calculator. For each student, the amount of time in seconds that they spent on the problem with each calculator was recorded. Is Calculator B likely to be a more effective device than Calculator A?
| Student | CalculatorA | Calculator B |
| 1 | 23 | 19 |
| 2 | 18 | 18 |
| 3 | 29 | 24 |
| 4 | 22 | 23 |
| 5 | 33 | 31 |
| 6 | 20 | 22 |
| 7 | 17 | 16 |
| 8 | 25 | 23 |
| 9 | 27 | 24 |
| 10 | 30 | 26 |
| 11 | 25 | 24 |
| 12 | 27 | 28 |
b) Please use step by step guidelines so I can follow in this excel problem: In the sheet entitled “Part 2 Question 7”, you will find the death rate (per 1,000 resident population) for random samples of counties in Alaska and Texas. Is the average death rate among Alaska counties likely to be lower than that among Texas counties?
| Alaska | Texas |
| 1.4 | 7.2 |
| 4.2 | 5.8 |
| 7.3 | 10.5 |
| 4.8 | 6.6 |
| 3.2 | 6.9 |
| 3.4 | 9.5 |
| 5.1 | 8.6 |
| 5.4 | 5.9 |
| 6.7 | 9.1 |
| 3.3 | 5.4 |
| 1.9 | 8.8 |
| 8.3 | 6.1 |
| 3.1 | 9.5 |
| 6 | 9.6 |
| 4.5 | 7.8 |
| 2.5 | 10.2 |
| 5.6 | |
| 8.6 |
In: Math
The head start program provides a wide range of services to
low-income children up to the age of 5 years and their families.
Its goals are to provide services to improve social and learning
skills and to improve health and nutrition status so that the
participants can begin school on an equal footing with their more
advantaged peers. The distribution of ages for participating
children is as follows 12% five-year-olds, 47% four-year-olds, 33%
three-year-olds, and 8% under three years. When the program was
assessed in a particular region, it was found that of the 215
randomly selected participants, 17 were 5 years old, 101 were 4
years old, 60 were 3 years old, 37 were under 3 years old. Perform
a test to see if there sufficient evidence at αα = 0.10 that the
region's proportions differ from the national proportions.
The correct hypotheses are:
The test value is (round to 3 decimal places)
The p-value is (round to 3 decimal places)
According to the Bureau of Transportation Statistics, on-time performance by airlines is described as follows:
| Action | % of time |
| On Time | 71 |
| National Aviation System Delay | 8 |
| Aircraft arriving late | 8 |
| Other (weather and other conditions) | 13 |
When a study was conducted it was found that of the 250 randomly
selected flights, 180 were on time, 18 were a National Aviation
System Delay, 20 arriving late , 32 were due to weather. Perform a
test to see if there is sufficient evidence at αα = 0.05 to see if
these differ from the governments statistics.
The correct hypotheses are:
The test value is (round to 3 decimal places)
The p-value is (round to 3 decimal places)
The head start program provides a wide range of services to
low-income children up to the age of 5 years and their families.
Its goals are to provide services to improve social and learning
skills and to improve health and nutrition status so that the
participants can begin school on an equal footing with their more
advantaged peers. The distribution of ages for participating
children is as follows 10% five-year-olds, 50% four-year-olds, 28%
three-year-olds, and 12% under three years. When the program was
assessed in a particular region, it was found that of the 202
randomly selected participants, 20 were 5 years old, 99 were 4
years old, 46 were 3 years old, 37 were under 3 years old. Perform
a test to see if there sufficient evidence at αα = 0.01 that the
region's proportions differ from the national proportions.
The correct hypotheses are:
The test value is (round to 3 decimal places)
The p-value is (round to 3 decimal places)
According to the Bureau of Transportation Statistics, on-time performance by airlines is described as follows:
| Action | % of time |
| On Time | 68 |
| National Aviation System Delay | 7 |
| Aircraft arriving late | 8 |
| Other (weather and other conditions) | 17 |
When a study was conducted it was found that of the 230 randomly
selected flights, 159 were on time, 21 were a National Aviation
System Delay, 21 arriving late , 29 were due to weather. Perform a
test to see if there is sufficient evidence at αα = 0.01 to see if
these differ from the governments statistics.
The correct hypotheses are:
The test value is (round to 3 decimal places)
The p-value is (round to 3 decimal places)
In: Math