62% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.
In: Math
1) A population of values has a normal distribution with μ = 97.3 and σ = 21.5 .
You intend to draw a random sample of size n = 42 .
A) Find the probability that a single randomly selected value is greater than 107.3. P(X > 107.3) =
Round to 4 decimal places.
B) Find the probability that the sample mean is greater than 107.3. P( ¯¯¯ X > 107.3) =
Round to 4 decimal places.
Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.
2) Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 11.3 years and a standard deviation of 1 years.
A) Find the probability that a randomly selected quartz time piece will have a replacement time less than 8.7 years? P(X < 8.7 years) = Enter your answer accurate to 4 decimal places.
Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
B) If the company wants to provide a warranty so that only 1.5% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty?
warranty = years Enter your answer as a number accurate to 1 decimal place.
Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
In: Math
A manufacturing process has two assembly lines, A and B. Suppose that line A produces 60% of the product. and line B produces the rest. We are told that 5% of the products produced by line A are defective in some way, and 8% of the line B products are defective. it may be helpful to construct a tree diagram with first and second-generation branches to answer the following:
C) if the end product is defective, what is the probability that it was produced by line B
In: Math
Census data for a city indicate that 64.4% of the under-18 population is white, 14.5% black, 19.5% Latino, 1.4% Asian, and 0.2% other ethnicities. The city points out that of 25,0092 police officers, 64.8% are white, 14.5% black, 19.1% Latino, and 1.4% Asian. Do the police officers reflect the ethnic composition of the city's youth? Test an appropriate hypothesis and state your conclusion. (Assume a significance level of alphaαequals=0.05)
A) Compute the chi-square statistic
B) Compute the P-Value
In: Math
The Gallup-Healthways Well-being Index is a comprehensive survey of the health status of Americans. A random sample of 2,580 adults were asked, "Have you ever been told by a physician or a nurse that you have depression?" Of these, 238 answered "Yes."
Using JMP construct the 99% confidence interval for the true proportion of Americans who have been told they have depression, and fill in the appropriate bounds in the confidence interval interpretation given below. Round your answers to two decimal places (i.e. 0._ _).
99% confident the true proportion of Americans who have been told by a physician or nurse they suffer from depression is between
and
Question 2 (1 point)
Refer to the scenario given in Question 1. According to the National Institute of Mental Health, 6.7% of adults suffer from depression. Is this percentage supported by the confidence interval found in Question1?
Question 2 options:
|
Yes, because 6.7% does not fall in the confidence interval. |
|
|
There is not enough information given to make a determination. |
|
|
No, because 6.7% does not fall in the confidence interval. |
Question 3 (1.5 points)
Question 3 options:
A study investigated ways to prevent staph infection in surgery patients. In a first step, researchers examined the nasal secretions of a random sample of 6,771 patients admited to various hospitals for surgery. They found that 1,251 of these patients tested positive for Staphylococcus aureus, a bacterium responsible for most staph infections.
Using JMP, find the 90% confidence interval for the true prorportion of patients admitted for surgery that tested positive for Staphylococcus aureus, and fill in the apporpriate bounds in the confidence interval interpretation given below. Round your answers to two decimal places (i.e. 0._ _).
90% confident the true proportion of patients admitted for surgery that tested positive for Staphylococcus aureus is between
and
Question 4 (1 point)
Saved
Refer to the scenario given in Question 3. Suppose a hospital does not have to implement any measures to control for staph infections if the percentage of patients who test positive for Staphylococcus aureus is less than 18%. Based on the confidence interval constructed in Question 3, does the hospital have to worry about controlling for staph infections?
Question 4 options:
|
Yes, because the entire confidence interval is not below 18%. |
|
|
Yes, because 18% is in the confidence interval. |
|
|
There is not enough information to make a determination. |
In: Math
Provide two columns of data that are related and demonstrate the Excel Scatterplot Correlation and Regression methodology. Which is the Independent and Dependent variable?
In: Math
2.51 Cards are drawn from a standard 52-card deck until an ace is drawn. After each card is drawn, it is put back in the deck and the cards are reshuffled so that each card drawn is independent of all others.
(a) Find the probability that the first ace is drawn on the 5th selection.
(b) Find the probability that at least 5 cards are drawn before the first ace appears.
(c) Repeat parts (a) and (b) if the cards are drawn without replacement. That is, after each card is drawn, the card is set aside and not replaced in the deck.
In: Math
Purpose: To explore the sampling distribution for sample proportions.
Materials: One package of candies with multiple colors (M&M’s – any variety, Skittles – any variety, Reese’s Pieces, etc.). You may select any size package but be mindful of the “sample size” which will vary depending on the type of candy you choose. You may want to purchase at least a king size package to ensure you end up with a sample size that is “large enough.” Select a color whose proportion you are interested in exploring in the candy you have chosen.
I have chosen the following candy: M&M'S Milk Chocolate
I have selected the following color: Brown
Step 1: Identify your hypotheses. Do some internet research to identify what the company claims the proportion of your selected color to be for the candy you have chosen. Provide the link for the internet source you used. The proportion of M&M'S Milk Chocolate that are brown is 0.13 according to https://blogs.sas.com/content/iml/2017/02/20/proportion-of-colors-mandms.html
Calculate the proportion of your candies that are the color you have selected. The proportion of my sample of 250 M&M'S Milk Chocolate that are brown is 0.6.
Compare your sample proportion to the company’s claim. Do you think the true population proportion is different from the company’s claim? Write the null and alternative hypotheses you would use to investigate the answer to that question. Write them in symbolic notation AND write each hypothesis statement in a sentence.
Step 2: Check the conditions for normality. Check the conditions and assumptions necessary to use the normal model as an approximation for the sampling distribution you are exploring. Show your work and verify whether you have met the criteria necessary to proceed. (Hint: If your sample size is not large enough, increase your sample size!) Remember there are three conditions you need to check.
Step 3: Use your sample evidence to test your hypotheses. Make a sketch of your sampling distribution. Label the mean and standard deviation (SE), marking at least two SE in each direction. Mark your sample proportion in the sketch and shade appropriately. Complete the hypothesis test using a significance level of 5% and analyze your results. Show all of your work!
Step 4: State your conclusion. What was the result of your hypothesis test? Give your final decision AND provide an interpretation in the context of this problem. Include all important details.
Step 5: Confidence Interval Now that you have tested the company’s claim and have come to some conclusion about it, you may be wondering, what really is the true portion of all these candies that are the color I chose? Create a 95% confidence interval to help you answer that question.Show all of your work!
Step 6: Write a sentence to describe the meaning of your confidence interval in the context of this problem. How does the interval you calculated compare to the company’s claim? Does it support the company’s claim or give evidence against it? How does this compare with the results of your hypothesis test?
In: Math
Find the median, quartiles, and make a histogram for the following data.
1,3,3,3,3,3,3,4,4,4,4,4,4,5,6,7,7,7,9,10,10,10,11,12,12,13,14,14,14,15,16,17,17,17,17,18,19,19,21,22,23,25,27,27,29, 32,35,35,36,45
In: Math
in 2010, the Maricopa Community College District's enrollment
data showed the following breakdown of students by ethnicity: 54.9%
White; 21.1% Hispanic; 7.9% Black; 4.5% Asian/Pacific Islander;
2.9% Native American; 8.8% Other. Information was collected from a
random sample 0f 300 students in 2017 to determine whether or not
the data has changed significantly. The sample data is given in the
table below. At the α=0.05 level of significance, test
the claim that the ethnic breakdown of students at MCCCD has not
changed significantly since 2010.
Which would be correct hypotheses for this test?
Ethnicity of students in sample:
| Ethnicity | Count |
|---|---|
| White | 137 |
| Hispanic | 71 |
| Black | 27 |
| Asian/Pacific Islander | 12 |
| Native American | 14 |
| Other | 39 |
Test Statistic:
Give the P-value:
Which is the correct result:
Which would be the appropriate conclusion?
In: Math
In: Math
3.50
Passedix is a game of chance played with three fair dice. Players bet whether the sum of the faces shown on the dice will be above or below ten. During the late sixteenth century, the astronomer and mathematician Galileo Galilei was asked by the Grand Duke of Tuscany to explain why “the chance of throwing a 9 with three fair dice was less than that of throwing a 10.” (Interstat, Jan. 2004) The grand duke believed that the chance should be the same because “there are an equal number of partitions of the numbers 9 and 10.” Find the flaw in the Grand Duke’s reasoning and answer the question posed to Galileo. Hint: What the Grand Duke was saying is: There are six ways to get a 9: 1+2+6; 1+3+5; 1+4+4; 2+2+5; 2+3+4; 3+3+3. There are also six ways to get a 10: 1+3+6; 1+4+5; 2+2+6; 2+3+5; 2+4+4; 3+3+4. [10 pts] 3.56 Two fair dice are tossed, and the following events are defined: A: {Sum of the numbers showing is odd} B: {Sum of the numbers showing is 9, 11, or 12} Are events A and B independent? Why? [10 pts]
In: Math
How would an error in the application of a "treatment" impact the results of a study....provide an example.
In: Math
To improve turnover (employees leaving your organization), you implemented a new training program company-wide about a year ago. However, you're not sure that the training is equally effective in reducing turnover between your service department, sales departments, and warehouse. To test this, you retrieved a list of all current and former employees that have received the training and created a dataset also recording their department. Conduct a test of independence to investigate this.
Turnover: Department:
former warehouse
current service
current sales
former warehouse
current sales
former sales
current sales
current service
former warehouse
current sales
current service
current warehouse
current service
current warehouse
current service
former sales
former sales
former service
The p-value for this chi-square was _____________and the chi-square value was _______________. This test _____________ achieve statistical significance. The expected value for Former Employee/Service was_________________, while the observed value was _______________________
options to fill in the blanks:
0.03, did, 2.33, did not, 0.33, 2.23, 1, 1.98.
In: Math
The commercial division of a real estate firm conducted a study to determine the extent of the relationship between annual gross rents ($1000s) and the selling price ($1000s) for apartment buildings. Data were collected on several properties sold. The data is...
| df | SS | MS | F | Significance F | |
| Regression | 1 | 41976.4 | |||
| Residual | 7 | ||||
| Total | 8 | 52373.2 | |||
| Coefficients | Standard Error | t Stat | P-value | ||
| Intercept | 19 | 3.2213 | 6.21 | ||
| Annual Gross Income | 7.75 | 1.457806668 | 5.31620562 |
(a) How many apartments are there?
(b) Write the estimated regression equation
(c) Use the t-test to determine whether the selling price is
related to annual gross rents. Use a=0.05
(d) Use the f-test to determine whether the selling price is
related to annual gross rents. Use a=0.05
(e) Predict the selling price of an apartment building with gross
annual rents of $52500
In: Math