Category: Mathematics Homework Help

Hypothesis testing is a challenging concept, indeed. First, let’s try to figure out the concept and how it works. Begin by answering these questions:

• What is the null hypothesis? Why do we want to reject our null hypothesis?
• The first step is the find the mean of our sample and compare it to the “hypothesized” mean of our null hypothesis—why do we do that?
• We use the results of our first step to calculate a test-statistic. Why is this important and how does it relate to the concept of z-score, which we learned a few weeks ago?
• What is a p-value? What role does it play in the rejection of the null hypothesis?
• What does it mean to reject the null hypothesis? Does that guarantee that the null hypothesis is false?

1. Lithium watch batteries of a certain brand are delivered to stores in batches of 100. The defective rate
in the population of such batteries is 1.5%.

(a) Calculate the mean and the standard deviation of the number of defective batteries in a randomly
selected batch.

(b) What is the probability that in a randomly selected batch there will be more than 1 defective batteries?

(c) The company incurs a loss of $8 for each defective battery. What is the expected loss per batch?
(d) Suppose now that there is an $8 loss for each defective battery, but there is a $6 reward for each batch
that has no defective batteries. Calculate the expected loss per batch.

2. A random sample of 40 station wagons and minivans sold in the USA in 2018 has been selected and the
collision-damage rating of each vehicle has been recorded. In this sample the average rating is 75 points(the
maximal possible rating is 100), and the sample standard deviation is 11.5 points. Create a 95% confidence
interval for the average rating of all wagons and minivans sold in the USA in 2018.

3. The objective of a study has been to decide whether consumers consider more price or quality. In a poll
of 2,000 American adults, 64% claimed that they mainly base their buying decisions on price.

(a) Construct a 99% confidence interval for the percentage of American adults who base their buying
decisions more on price than quality.

(b) Suppose that you decrease the confidence level from 99% to a smaller probability. How would the left
endpoint change ( increase or decrease)? How would the right endpoint change (increase or decrease)?

4. In a survey for a future election a random sample of size 100 has been selected. Within that sample 8%
said that they will vote candidate A.

(a) Test the hypothesis that candidate A will receive more than 6% of the vote in the election. Make
the alternative hypothesis that the proportion of votes candidate A will receive is more than 6%. Use 5%
significance level.

(b) Calculate the p-value of the above test.

(c) What would be your decision if in question (a) the significance level had been 1%?

5. It has been determined that the population average household income in a county is µ = 80, 000, and the
population standard deviation σ = 7, 000. Let X¯ be the average income in a random sample of 60 households
from that county.

(a) What is the mean and the standard deviation of X¯?
1

(b) Find the probability that X¯ will be larger than 82,000.

(c) What is the probability that the total income in the sample of 60 is less than 4,740,000?

6. The US Food and Drug Administration wants to estimate the proportion of the US population having
diabetes with a 99% confidence interval. They want the width of the confidence interval (the difference
between the right endpoint and the left endpoint) to be no more than 0.02. Determine the necessary sample
size in order to achieve this objective. Assume that they have no initial information for the true population
proportion prior to the study.

7. In a casino there is a roulette wheel with 18 black slots, 18 red slots, and 2 slots without color (these are
called zero and double zero). If a player puts k dollars on red, and the ball stops in one of the red slots,
then the player receives back the k dollars she put on the table, plus an additional k dollars (so, in effect,
she wins k dollars). If the ball stops in a black slot or in a slot without color, then she loses the k dollars
she placed on the table. Player A follows a doubling strategy: first she bets $1 on red, if she loses she bets
$2 on red, if she loses again she bets $4 on red, etc. She quits the first time the ball stops in a red slot, or
when she loses all her money, whichever happens first. Initially she has 63 dollars. Calculate the expected
loss of player A.

Gender-Career IAT Variables

Row Variable: Birth-Gender
Column Variable: Assoc-Gen-Career

Gender-Career IAT variable descriptions (opens in a new tab).

https://www.statcrunch.com/app/index.php?dataid=37…

Prompt

• Use StatCrunch to produce a two-way contingency table as we did in Unit 4 (Module 11). Use the row variable and the column variable listed above for your IAT data set.
  • Copy the table in your StatCrunch output window and paste it in the textbox with your response.
  • After you paste the content of your StatCrunch output window into the textbox, keep the table titled Contingency table results, and delete the Chi-Square results table.
  • VERY IMPORTANT: Perform each of the following to make your table more meaningful to the reader (and me, the grader). If your table is not meaningful, I cannot check (and therefore grade) your work.
    • Above your contingency table, provide a meaningful title that includes the name of your IAT Data set.
    • The row and column labels in the contingency table are numbers. This makes the two-way table hard to read. Use the variable descriptions for your IAT data set to relabel the column and rows with meaningful words. (The variable description link for your IAT data set is provided above in the Variables section.) Not sure how to relabel the columns in rows in your two-way table? Here is an example (opens in a new tab).
    • Below the table, include the name of your row variable and the name of your column variable.

2.) For each of the following percentage questions, copy the question for your IAT data set and paste it into the textbox. Then find the indicated percentage. Write each percent as a ratio (e.g. 25 out of 40) and as a percentage (e.g. 25/40 = 62.5%). Then interpret the percentage in a sentence.

A.) Find this percentage only for your IAT data set.
Gender-Career IAT: What percentage of IAT participants were born female?

B.) Find this percentage only for your IAT data set.
Gender-Career IAT: What percentage of the IAT participants indicated that they moderately or strongly associate males with career?

C.) Find this percentage only for your IAT data set.
Gender-Career IAT: What percentage of born-males moderately or strongly associate females with career?

D.) Find this percentage only for your IAT data set.
Gender-Career IAT: What percentage of participants who moderately associate females with career were born female?

3.) Copy the question below for your IAT data set and paste it into the textbox. Then answer this question.

Gender-Career IAT: Are born-male participants more likely to indicate that they associate neither males nor females with career?

4.) In the Variables section above, use the variable descriptions link to peruse the variables in your chosen IAT data set. Does your unique data set contain any continuous random variables? If so, give an example and explain why the variable is a continuous random variable. If not, explain why not?

5.) In the Variables section above, use the variable descriptions link to peruse the variables in your chosen IAT data set. Does your unique data set contain any discrete random variables? If so, give an example and explain why the variable is a discrete random variable. If not, explain why not?

The use of statistics is often employed to highlight international, national, and state trends in crime and drug abuse.

1. Explain the following terms in your own words.

1. Box-and-whiskers plot
2. Standard deviation
3. Normal distribution

(9 points)

2. A BAC describes the amount of alcohol in a person’s blood, expressed as weight of alcohol per unit of volume of blood. For example, 0.08 percent BAC indicates 80 mg of alcohol per 100 ml of blood.” (source: http://www.austintexas.gov/faq/what-does-blood-alcohol-concentration-bac-measure (Links to an external site.); please note, you do not require to access the source to answer the question)

For the data set below calculate the mean, median, mode and standard deviation.

Then, for Blood alcohol levels only, plot:

a. Frequency histogram

b. Probability (i.e. cumulative frequency) plot

What do you conclude about the distribution of the sample?

From the data set presented here, would you feel comfortable to say that the age group between 30-39 years exhibits higher BAC counts than other age groups?

(16 points)

• In an experiment using three tosses of the same coin, state and apply the general equation that provides the total number of possible outcomes for the experiment and list the outcome string (3 points). Then, for each of the following three scenarios, list the possible outcome string and calculate the probability of the scenario as a decimal number (to three places) showing all working (9 points).
  • The probability of getting three heads when flipping a coin 3 times.
  • The probability of at least getting one head and one tail when flipping a coin 3 times.
  • The probability of getting a head in the first flip, a tail in the second, and a head again in the third flip of a coin.
• Below is an incomplete contingency table displaying two levels for each the gender and the political party association (13 points).
  • Complete the table with all marginal totals and cell counts.
  • Calculate the following probabilities.
    • For a male to be a Republican.
    • For a voter to be female.
    • For a voter to be either a democrat or a female.
    • For a person to not be a female but voting democratic.

I’m working on a probability practice test / quiz and need guidance to help me learn.

need someone who can provide answers for this short MCQs. need answers as A,B C or D ONLY. Calculations not required.

I’m working on a calculus practice test and need clear and concise working and answers to help me study.
Test will be on Parametric Equations and Polar Coordinates.

Prompt

1. Based on a recent study of college students, the average student loan debt amount is $4000. Is the mean student loan debt higher at StatCrunchU? Include each of the following in your response. (see concepts in Units 7 & 8 – Modules 17-23)
   • State your hypotheses in symbolic form and in words.
   • Verify that normality conditions are met. Which teest are you using? Why?
   • Use StatCrunch to conduct the hypothesis test. Copy and paste the results (the StatCrunch output window) into your response.
   • Give your P-value and interpret its meaning.
   • State a conclusion that answers the research question. Use a significance level of 5%.

StatCrunch Resources

Here is a PDF document with all StatCrunch directions

How & What to Turn In

Submit your answers to the prompt above. Make sure to include any StatCrunch graphs and tables in your answer. Turn in your work by typing your response and embedding your graphs/tables into the textbox below (just like we have done in our discussion boards). When you are ready to submit your work, click on Submit Assignment.

Find an article that mentions a new drug that promises an improved survival rate.

• Identify whether this rate represents the mean or the median of the data set.
• Assess whether that is ideally what you’d want to know for this data.
• Provide a specific reason for your answer.

1. Consider the system
x˙ = (x − h)(r − x).
(a) Draw a stability diagram in the (r, h)-plane. Be sure to indicate the types of
bifurcation curves/points.
(b)Draw phase portraits for each qualitatively different choice of (r, h).

2. For each parameter r, consider the following flow on the circle:
˙θ = cos2
(θ) + r
(a) Find all bifurcation points (r
∗
, θ∗
).
(b) Draw all qualitatively different phase portraits. What type of bifurcation occurs
at the bifurcation points?
(c) Find the period of oscillation when r is small and positive.