Here is a random sample of the body temperature of 25 young adults.
| 96 | 96.6 | 96.7 | 96.9 | 97 |
| 97.1 | 97.1 | 97.2 | 97.3 | 97.4 |
| 97.4 | 97.7 | 97.7 | 97.7 | 97.8 |
| 97.9 | 98 | 98 | 98.2 | 98.2 |
| 98.3 | 98.3 | 98.7 | 98.8 | 98.9 |
Complete the relative frequency distribution table.
| Temperature Group | Frequency | Relative Frequency | Cumulative |
|---|---|---|---|
| 96 ≤ x < 96.41 | 1 | 1/25 | |
| 96.41 ≤ x < 96.82 | 2 | 2/25 | |
| 96.82 ≤ x < 97.23 | 5 | 5/25 | |
| 97.23 ≤ x < 97.64 | 3 | 3/25 | |
| 97.64 ≤ x < 98.05 | 7 | 7/25 | |
| 98.05 ≤ x < 98.46 | 4 | 4/25 | |
| 98.46 ≤ x < 98.87 | 2 | 2/25 | |
| 98.87 ≤ x < 99.28 | 1 | 1/25 |
In: Math
Data are collected on the relationship between the number of hours per week practicing a musical instrument and scores on a math test. The line of best fit is as follows: ŷ = 72.5 + 2.8x.
What would you predict the score on a math test would be for a student who practices a musical instrument for 1.2 hours a week? Round to one decimal place.
In: Math
Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are equal (sigma1 = sigma2), so that the standard error of the difference between means is obtained by pooling the sample variances. A paint manufacturer wanted to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. Construct a 99% confidence interval for mu1 - mu2, the difference between the mean drying time for paint type A and the mean drying time for paint type B.
In: Math
An advertisement for A-1 Motor Oil states that in a survey of auto mechanics across the country, the majority of them use A-1 Motor Oil in their own vehicles.
a. correlation does not imply causality b. voluntary response survey c. self-interest survey d. poorly worded questions
In: Math
In Nebraska, the average ACT score is 21.7 with a standard deviation of 1.1. We collect a random sample of 30 students who took the exam last year.
Part 1: (6 pts)
Check the all necessary conditions in detail (not just yes or no) (1 pt each) and give the sampling model and parameters to 2 decimal places (2 pts).
Part 2: (8 pts)
What is the probability that the average composite ACT score is 22.1 or more? Show your calculations for finding the z-score to three decimal places (4 pts), then find the probability to four decimal places using the appropriate probability notation (2 pts). Write a sentence that gives your solution in context (2 pts).
In: Math
a. Explain why you would also like to know the standard deviations of the battery lifespans before deciding which brand to buy.
b. Suppose the standard deviations are 2 hours for DuraTunes and 1.5 hours for RockReady. You are headed for 8 hours at the beach. Which battery is most likely to last all day? Explain.
PLEASE SHOW ALL WORK AND RATIONALE.
TYPED WORK ONLY PLEASE
NO HANDWRITTEN.
In: Math
Eight samples (m=8) have been collected from a manufacturing process that is in statistical control, and the dimension of interest has been measured for each part. It is desired to determine the values of the center, LCL, and UCL for ?̅ and R charts. The calculated ?̅ values (units are in mm) are 2.723, 1.993, 2.008, 1.723, 1.999, 2.001, 1.995 and 2.723 The calculated R values (mm) are 0.015, 0.021, 0.020, 0.023, 0.723, 0.723, 0.014 and 0.011. Also plot the control chart. Comment on your answer.
In: Math
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:
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Yes, because the entire confidence interval is not below 18%. |
|
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Yes, because 18% is in the confidence interval. |
|
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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