Make a simulation to verify the following theorem: if X1 ∼ N(µ1, (σ 1)^2 ), X2 ∼ N(µ2, (σ2)^ 2 ), and X1 and X2 are independent, then X1 + X2 ∼ N(µ1 + µ2, (σ2)^2+ (σ 2 )^2 ).

Please discuss why statistics are important today. In your response, include a statistic that is important to you. How do you know this statistic is valid?

Note that this response needs to be at least 200-300 words.

Suppose we have the process (time series)
xt = 0.5wt-1 + wt;
where wt is white noise with mean zero and variance sigma squared w.

Find the mean, variance, autocovariance, and ACF of xt.

An ANOVA procedure was performed on a data-set containing information on land values in five neighboring counties. The analysis indicated that at least one pair of land values was significantly different from each other. The LSD was found to be $185/acre at the 5% confidence level. Data for the five counties are listed below. Which county land values are significantly different from each other? Be sure to use terminology such as significantly higher or significantly lower in your descriptions.  

10. According to the National Health and Nutrition Examination Survey and the Epidemiologic Follow-up Study the mean systolic blood pressure for individuals aged 25 to 59 is 127.3 with a standard deviation of 20.2. A sample measurement of systolic blood pressure from 15 Statistics students is taken to learn whether students have blood pressure that differs from the national average.

(a) Perform a one sample Z test on these data to learn whether a difference in blood pressure exists:

• present calculated Z test value, and

• write a brief conclusion about your finding. Use α = .05 for hypothesis testing.

(b) Construct a 95% confidence interval about the sample mean for these data.

Sample Systolic Blood Pressure

An existing inventory for a test measuring self-esteem indicates that the scores have a standard deviation of

10

. A psychologist gave the self-esteem test to a random sample of

100

individuals, and their mean score was

65

. Construct a

99%

confidence interval for the true mean of all test scores. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a  list of formulas.)

A leasing firm claims that the mean number of miles driven annually, μ, in its leased cars is less than 12700 miles. A random sample of 25 cars leased from this firm had a mean of 12031 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 2800 miles. Assume that the population is normally distributed. Is there support for the firm's claim at the 0.01 level of significance? Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.)

A certain test for a particular type of cancer is known to be 95% accurate. A person takes the test and the results are positive. Suppose the person comes from a population of 100,000 where 2000 people suffer from that disease.

What if the person takes a second test and result is still positive, what can we conclude about his odds of having cancer?

One attempt was to investigate the effect of two treatments on the formation of tartar in dogs. In addition to the two treatment groups, there was also a control group. in the trial included 26 dogs randomized to one of the three treatment groups (follow normal distribution):

1. P2O7

2. HMP

3. Control (standard feed)

the values are given:

Group 1=(P2O7) 2= (HMP) 3=(Kontrol)

ni 9 8 9

mean 0.7467 0.4375 1.0889

s^2 0.13655 0.08448 0.17854

question: Use Bartletts test to test if the variance are equal

If possible answer in R. If not by hand is also good.

1. For each the following questions,

• Define the appropriate parameter(s)

• State ?! and ?!

• Choose the correct model from the following list:

  1. Test for a single mean

  2. Test for a single proportion

  3. Test for two means, independent samples

  4. Test for mean difference, dependent sampling

  5. Test for two proportions, independent samples

1. You want to support the claim that male bass singers are taller than male tenor singers. Parameter(s):

   Hypotheses: ?!: __________________ ?!: __________________ Model to use: ______

2. You want to reject the claim that no more than 10% of students will suffer financial hardship if tuition

   increased. Parameter(s):

   Hypotheses: ?!: __________________ ?!: __________________ Model to use: ______

3. You want to support the claim that people spend, on average, more time on the Internet than they do

   watching television. 200 people will be asked how much time they spent on the TV and on the Internet. Parameter(s):

   Hypotheses: ?!: __________________ ?!: __________________ Model to use: ______

4. You want to test the claim that the average age for a community college student is over 27. You want to

   support this claim and sample 20 students. Parameter(s):

   Hypotheses: ?!: __________________ ?!: __________________ Model to use: ______

5. Is there a difference in mean overall quality of tomatoes bought at farmers markets versus at grocery

stores? Tomatoes are purchased at 30 randomly selected farmers markets and 40 randomly selected high- end grocers. Their mean overall quality is compared.

Parameter(s):

Hypotheses: ?!: __________________ ?!: __________________ Model to use: ______

6. A hospital surgery review board wants to determine if the proportion of patients undergoing a particular surgery who are cured is greater than the proportion that are cured by the current non-surgical standard treatment.

   Parameter(s):

   Hypotheses: ?!: __________________ ?!: __________________ Model to use: ______

7. A higher education centered non-profit organization wants to determine if the percentage of entering

   freshmen that graduate is lower at a public university than at a private college. Parameter(s):

   Hypotheses: ?!: __________________ ?!: __________________ Model to use: ______

8. Does the home team have an advantage in NBA basketball games? In a study of 25 games, the visiting

   team’s points were compared to the home team’s points. Parameter(s):

   Hypotheses: ?!: __________________ ?!: __________________ Model to use: ______

9. A hypothesis test is performed to determine if recent female college graduates are subject to pay discrimination, earning less on average for similar work than recent male college graduates with similar qualifications.

   Parameter(s):

Hypotheses: ?!: __________________ ?!: __________________ Model to use: ______

according to lear center local news archive the average amount of time that a half hour local tv news broadcast devotes to us foreign policy, including the war in iraq, is 38 seconds. (time, february 28, 2005). suppose a random sample of 40 such half-hour news broadcasts shows that an average of 38 seconds are devoted to us foreign policy with a standard deviation of 9 seconds. Find a 95% confidence interval for the mean time that all half-hour local TV news broadcasts devote to U.S. foreign policy.

Data can be collected and organized as an ordered pair (x, y). The data can be analyzed to determine the type and strength of a correlation and to calculate a regression line in order to make a prediction.

Use the internet to find a data set of ordered pairs. Key terms to search: Free Public Data Sets and Medical Data Sets.

Create a Post:

Introduce your Data Set.

1. Which would be the independent variable, and which would be the dependent variable?
2. Without drawing a scatter plot, would you expect a positive, negative or no correlation? Explain.
3. Would you categorize your data to have a strong or weak correlation? Why?
4. What would the r² value tell you about the data that you selected?
5. What is the equation of the regression line?
6. Use the regression line to make a prediction about the data you collected.

Using the following data below, answer parts a-b. Do women feel differently from men when it comes to tax​ rates? One question on a survey of randomly selected adults​ asked, "What percent of income do you believe individuals should pay in income​ tax?" Test whether the mean tax rate for females differs from that of males at the a=0.01 level of significance.

A) Find the test statistic for this hypothesis test.

B) Determine the​ P-value for this test.

Data: