: An observational study is conducted to investigate the association between age and total serum cholesterol. The correlation is estimated at r = 0.35. The study involves n=125 participants and the mean (std dev) age is 44.3 (10.0) years with an age range of 35 to 55 years, and mean (std dev) total cholesterol is 202.8 (38.4).
a. Estimate the equation of the line that best describes the association between age (as the independent variable) and total serum cholesterol.
b. Estimate the total serum cholesterol for a 50-year old person.
c. Estimate the total serum cholesterol for a 70-year old person.
d. For part c, why or why not might this estimate be appropriate?
In: Math
1. Weakly earnings on a certain import venture are approximately normally distributed with a known mean of $487 and unknown standard deviation. If the proportion of earnings over $517 is 27%, find the standard deviation. Answer only up to two digits after decimal.
2.X is a normal random variable with mean μ and standard deviation σ. Then P( μ− 1.4 σ ≤ X ≤ μ+ 2.2 σ) =? Answer to 4 decimal places.
3.Suppose X is a Binomial random variable with n = 32 and p = 0.41.
Use binomial distribution to find the exact value of P(X < 11). [Answer to 4 decimal places]
| 错误. | Tries 1/5 | 以前的尝试 |
What are the appropriate values of mean and standard deviation
of the normal distribution used to approximate the binomial
probability?
μ = 13.12, and σ = 0.087.
μ = 13.12, and σ = 2.782.
μ = 13.12, and σ = 7.741.
μ = 32, and σ = 0.41.
| Tries 0/3 |
Using normal approximation, compute the approximate value of P(X < 11). [Answer to 4 decimal places]
| Tries 0/5 |
Is the n sufficiently large for normal
approximation?
Yes, because n is at least 30.
No, because μ±3σ, is contained in the interval (0, 32).
Yes, because μ±3σ, is inside the interval (0, 32).
No, because np < 15
4. Usually about 65% of the patrons of a restaurant order burgers. A restaurateur anticipates serving about 155 people on Friday. Let X be the numbers of burgers ordered on Friday. Then X is binomially distributed with parameters n = 155 and p = 0.65.
What is the expected number of burgers (μX) ordered on Friday? [Answer up to 2 digits after decimal]
| Tries 0/5 |
Find the standard deviation of X (σX)? [Answer up to 3 digits after decimal]
| Tries 0/5 |
If the restaurant ordered meats to prepare about 109 burgers for Friday evening. Use normal approximation of binomial distribution to find the probability that on Friday evening some orders for burgers from the patron cannot be met. [Answer up to 4 digits after decimal]
| Tries 0/5 |
How many burgers the restaurant should prepare beforehand so that the chance that an order of burger cannot be fulfilled is at most 0.05? i.e. Find a such that P(X > a) = 0.05 using normal approximation of binomial distribution.
In: Math
Problem 8: The Framingham Heart Study was a longitudinal cohort study of 5000+ men and women. One outcome of interest was fasting glucose levels. Glucose levels were categorized into three different categories:
Glucose Levels
-Diabetes (glucose >126),
-Impaired Fasting Glucose (glucose 100-125),
-Normal Glucose
Several possible risk factors were also recorded:
Risk Factors
-Sex
-Age
-BMI (normal weight, overweight, obese)
-Genetics
To determine if each possible risk factor is related to glucose levels,researchers need to use an appropriate hypothesis test.
Test Choices
1. ANOVA
2. Chi-Square GOF
3. Chi-Square test for independence
4. Test for equality of means
5. Test for equality of proportions
6. Other
a. What test would be used to assess whether the different sexes(male and female) have the same proportions of the different glucose levels?
b. What test would be used to assess whether the different glucose levels have the same mean age?
c. What test would be used to assess whether the different categories of BMI have the same proportions of the different glucose levels?
In: Math
which statistical analysis to use for a survey of 5 questions with four choices each strongly positive, positive, neutral and negative
In: Math
How does confidence intervals confirm hypothesis testing results. Provide an example
In: Math
Use the applet "Sample Size and Interval Width when Estimating Proportions" to answer the following questions.
This applet illustrates how sample size is related to the width of a 95% confidence interval estimate for a population proportion.
(a)
At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.023?
(b)
As the sample size decreases for any given confidence level, what happens to the confidence interval?
The width of the confidence interval becomes the same as the standard error.The confidence interval becomes more narrow because the sampling distribution becomes larger. The confidence interval becomes wider because the standard error becomes larger.The confidence interval becomes wider than the population proportion.The confidence interval becomes more narrow than the population proportion.
In: Math
You work for a lobby group that is trying to convince the government to pass a new law. Before embarking on this, your lobby group would like to know as much as possible about the level of community support for the new law.
Your colleague, based on his research into community opinion on related matters, proposes that 32% of the community support the law. You decide to survey 100 people, and find that 27% of this survey support the law.
a)Based on the assumption that the population proportion is 32%, calculate the z-score of the sample proportion in your survey. Give your answer as a decimal to 2 decimal places.
z =
b)Determine the proportion of the standard normal distribution that lies to the left of this z-score. That is, determine the area to the left of this z-score in the standard normal distribution. You may find this standard normal table useful. Give your answer as a percentage to 2 decimal places.
Area = %
c)Denote by x% the percentage proportion you calculated in part b). Consider the following five potential conclusions:
A: There is a chance of x% that your friend is correct, that the true population proportion is 32%.
B: If your colleague is correct and the true population proportion is 32%, then x% of all samples will produce a sample proportion of 27% or lower.
C: If your colleague is correct and the true population proportion is 32%, then x% of all samples will produce a sample proportion of 27% or higher.
D: There is a chance of x% that the true population proportion is 32% or lower.
E: There is a chance of x% that the true population proportion is 32% or higher.
Select the statement that can be inferred from your findings:
A
B
C
D
E
In: Math
1. a)What is your null hypothesis regarding sepal lengths for
the two species? And what is your alternate hypothesis?
b) Describe your hypotheses in terms of your test statistic: what
would be the t under the null hypothesis, H0, and what
would be the statement about t under your alternate hypothesis
Ha? Would you do a one- or non-(i.e.,
two-sided) directional test? Why?
| Sepal.Length | Species |
| 6.1 | versicolor |
| 6.3 | versicolor |
| 6.1 | versicolor |
| 5.5 | versicolor |
| 5.5 | versicolor |
| 5.8 | versicolor |
| 5.8 | versicolor |
| 5 | versicolor |
| 5.6 | versicolor |
| 5.7 | versicolor |
| 5.7 | versicolor |
| 6.2 | versicolor |
| 5.1 | versicolor |
| 5.7 | versicolor |
| 6.3 | virginica |
| 7.7 | virginica |
| 6.3 | virginica |
| 6.7 | virginica |
| 6.1 | virginica |
| 7.7 | virginica |
| 6.3 | virginica |
| 6.4 | virginica |
| 6 | virginica |
| 6.9 | virginica |
| 6.3 | virginica |
| 6.5 | virginica |
| 6.2 | virginica |
| 5.9 | virginica |
In: Math
Find the minimum sample size n needed to estimate μ for the given values of c, σ, and E.
c=0.95, σ=7.2, and E=1
Assume that a preliminary sample has at least 30 members.
n=___ (Round up to the nearest whole number.)
In: Math
Because some people are unable to stand to have their height measured, doctors use the height from the floor to the knee to approximate their patients’ height (in cm).
| Height of Knee | Overall Height |
| 57.7 | 192.3 |
| 47.5 | 153.3 |
| 43.5 | 146.2 |
| 44.8 | 160.4 |
| 55.6 | 171.4 |
| 54.9 | 176.7 |
a. Use Excel to determine the correlation coefficient of this data
b. Use Excel to determine the regression equation of this data
c. Find the overall height from a knee height of 45.3 cm
d. Find the overall height from a knee height of 52.7 cm
In: Math
Use R studio to do this problem. This problem uses the wblake data set in the alr4 package. This data set includes samples of small mouth bass collected in West Bearskin Lake, Minnesota, in 1991. Interest is in predicting length with age. Finish this problem without using Im()
(a) Compute the regression of length on age, and report the estimates, their standard errors, the value of the coefficient of determination, and the estimate of variance. Write a sentence or two that summarizes the results of these computations
(b) Obtain a 99% confidence interval for from the data. Interpret this interval in the context of the data.
(c) Obtain a prediction and a 99% prediction interval for a small mouth bass at age 1 . Interpret this interval in the context of the data.
In: Math
The following data represent the calories and sugar, in grams, of various breakfast cereals.
|
Product |
Calories |
Sugar |
|
|---|---|---|---|
|
A |
350 |
9.7 |
|
|
B |
410 |
4.5 |
|
|
C |
430 |
24.0 |
|
|
D |
490 |
25.0 |
|
|
E |
540 |
22.6 |
|
|
F |
550 |
24.7 |
|
|
G |
590 |
22.2 |
Use the data above to complete parts (a) through (d).
a. Compute the covariance.
b. Compute the coefficient of correlation.
c. Which do you think is more valuable in expressing the relationship between calories and
sugar—the covariance or the coefficient of correlation? Explain.
d. What conclusions can you reach about the relationship between calories and sugar?
In: Math
One of the questions Rasmussen Reports included on a 2018 survey of 2,500 likely voters asked if the country is headed in right direction. Representative data are shown in the DATAfile named RightDirection. A response of Yes indicates that the respondent does think the country is headed in the right direction. A response of No indicates that the respondent does not think the country is headed in the right direction. Respondents may also give a response of Not Sure.
(a)What is the point estimate of the proportion of the population of respondents who do think that the country is headed in the right direction? (Round your answer to four decimal places.)
(b)At 95% confidence, what is the margin of error for the proportion of respondents who do think that the country is headed in the right direction? (Round your answer to four decimal places.)
(c)What is the 95% confidence interval for the proportion of respondents who do think that the country is headed in the right direction? (Round your answers to four decimal places.)
___to ___
(d)What is the 95% confidence interval for the proportion of respondents who do not think that the country is headed in the right direction? (Round your answers to four decimal places.)
____ to ____
(e)Which of the confidence intervals in parts (c) and (d) has the smaller margin of error? Why?
The confidence interval in part (c) has a (Smaller or Larger) margin of error than the confidence interval in part (d). This is because the sample proportion of respondents who do think that the country is headed in the right direction is (closer to .5 / closer to 1 / farther from .5 / farther from 1) than the sample proportion of respondents who do not think that the country is headed in the right direction.
Dataset:
553 - No
70 - Not Sure
384 - Yes
In: Math
Consider the following hypothesis test.
| H0: μ ≤ 25 |
| Ha: μ > 25 |
A sample of 40 provided a sample mean of 26.8. The population standard deviation is 6.
(a)
Find the value of the test statistic. (Round your answer to two decimal places.)
(b)
Find the p-value. (Round your answer to four decimal places.)
p-value =
(c)
At
α = 0.01,
state your conclusion.
Reject H0. There is sufficient evidence to conclude that μ > 25.Reject H0. There is insufficient evidence to conclude that μ > 25. Do not reject H0. There is sufficient evidence to conclude that μ > 25.Do not reject H0. There is insufficient evidence to conclude that μ > 25.
(d)
State the critical values for the rejection rule. (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)
test statistic≤test statistic≥
State your conclusion.
Reject H0. There is sufficient evidence to conclude that μ > 25.Reject H0. There is insufficient evidence to conclude that μ > 25. Do not reject H0. There is sufficient evidence to conclude that μ > 25.Do not reject H0. There is insufficient evidence to conclude that μ > 25.
In: Math
The two-sample t-test is applied to compare whether the average difference between two groups is significant or if it is due instead to random chance.
Use good references,
1. Briefly, describe the difference between Unpaired Two-Sample T-test and Paired Two-Sample T-test.
2. Provide an application example for Unpaired Two-Sample T-test, and stablish the Ho and Ha Hypotheses.
3. Provide an application example for Paired Two-Sample T-test, and stablish the Ho and Ha Hypotheses.
4. Explain the purpose of P-values and its application in the context of your two examples.
In: Math