A variable of two populations has a mean of 7.9 and a standard deviation of 5.4 for one of the populations and a mean of 7.1 and a standard deviation of 4.6 for the other population. a. For independent samples of sizes 3 and 6, respectively, find the mean and standard deviation of x1 - x2.b. Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Explain your answer.c. Can you conclude that the variable x1 - x2 is normally distributed? Explain your answer.

Question

A variable of two populations has a mean of 7.9 and a standard deviation of 5.4 for one of the populations and a mean of 7.1 and a standard deviation of 4.6 for the other population.

a. For independent samples of sizes 3 and 6, respectively, find the mean and standard deviation of x1 - x2.
b. Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Explain your answer.
c. Can you conclude that the variable x1 - x2 is normally distributed? Explain your answer.

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Statistics

Advanced Topics in Statistics

Related Statistics Q&A

Find answers to questions asked by students like you.

Q: The times ( in seconds) for a sample of seven sports cars to accelerate from 0 to 60 miles per hour ...

A: The number of standard deviation is 3.8 away from the mean is obtained below:From the data set 3.8 h...

Q: Suppose that, in a hypothesis test, the null hypothesis is in fact true. a. Is it possible to make a...

A: Type I error:Probability of rejecting the null hypothesis when it is actually true.Type II error:Pro...

Q: In each of Exercises, we have presented a confidence interval (CI) for the difference, µ1 - µ2, betw...

A: It is given that the 95% confidence interval is -20 to -15.

Q: Poisson: Deaths Currently, an average of 7 residents of the village of Westport (population 760) die...

A: Note:Hey there! Thank you for posting the question. However, since your question has more than 3 sub...

Q: If you obtained one thousand 95% confidence intervals for a population mean, µ, roughly how many of ...

A: Solution: We have to determine:If we obtained one thousand 95% confidence intervals for a population...

Q: I need help with only question 14. I need help with parts a,b,c,d, and e.

A: Hey there! Thank you for posting the question. Since there are multiple subparts posted, according t...

Q: What test statistic is used for a hypothesis test that the population regression coefficient for the...

A: Test statistic and distribution for hypothesis test that population regression coefficient is zero:T...

Q: Regarding the criterion used to decide on the plane that best fits a set of data points in k + 1 dim...

A: a)Least-square criterion:The least-square criterion is the criterion using which it is determined th...

Q: The P-value for a hypothesis test is 0.083. For each of the following significance levels, decide wh...

A: Decision criterion:If the p-value of the test is less than or equal to the level of significance, re...

Q: Testing Claims About Variation. In Exercises 5–16, test the given claim. Identify the null hypothesi...

A: Click to see the answer

Q: Blood Pressure Medication. A medical researcher wants to determine factors that affect a patient’s r...

A: (a)Justification:Response variable:Response variable in a regression equation is the dependent varia...

Q: Suppose x1 and x2 are predictor variables for a response variable y. a. The distribution of all poss...

A: a)

Q: Powerball: Poisson Approximation to Binomial There is a 1/292,201,338 probability of winning the Pow...

A: Requirements for using the Poisson distribution as an approximation to binomial distribution are as ...

Q: Technology. In Exercises 9–12, test the given claim by using the display provided from technology. U...

A: The claim is to test that the mean of tornado length is greater than 2.5 miles at 5% level of signif...

Q: Define the phrase independent samples.

A: Independent samples:These samples are randomly selected from the population. It does not depends on ...

Q: Births In a recent year, NYU-Langone Medical Center had 4221 births. Find the mean number of births ...

A: Mean of Poisson distribution:The formula is given by,

Q: State two reasons why including the P-value is prudent when you are reporting the results of a hypot...

A: Click to see the answer

Q: In the past, the value of houses a local realtor has sold is normally distributed with a mean of $25...

A: It is given that the value of houses is normally distributed with mean 252,000 and standard deviatio...

Q: What plots did we use in this module to decide whether it is reasonable to presume that assumptions ...

A: From the given question,It is known that the residual plot is the most reasonable plot or condition ...

Q: Testing Claims About Proportions. In Exercises 9–32, test the given claim. Identify the null hypothe...

A: It is given that in super bowl wins, 28 out of 49 were won by NFC. Also, the level of significance i...

Q: In each of Exercises, we have provided a scenario for a hypothesis test for a population mean. Decid...

A: Click to see the answer

Q: Regarding the variables in a multiple linear regression analysis: a. What is the dependent variable ...

A: a).Response variable:Response variable in a regression equation is the dependent variable, which can...

Q: Cheese Consumption. The U.S. Department of Agriculture reports in Food Consumption, Prices, and Expe...

A: (a)Null hypothesis:Null hypothesis is a statement which is tested for statistical significance in th...

Q: Testing Claims About Variation. In Exercises 5–16, test the given claim. Identify the null hypothesi...

A: The null and the alternative hypotheses are,H0: σ=0.0230 (The standard deviation of the weights for ...

Q: Testing Claims About Variation. In Exercises 5–16, test the given claim. Identify the null hypothesi...

A: Chi square:The test statistic formula for the chi square distribution is,

Q: Consider the quantities µ1, σ1, x1, s1, µ2, σ2, x2, and s2. a. Which quantities represent parameters...

A: (a)Parameter:Any statistical measure based on all units in the population is called Parameter.

Q: Cans of Coke: Confidence Interval  If we use the data given in Exercise 1, we get this 95% confidenc...

A: The 95% confidence interval for the new filling process is 0.1846 oz. < σ < 0.4900 oz.

Q: Technology. In Exercises 9–12, test the given claim by using the display provided from technology. U...

A: The null and the alternative hypotheses are,H0: µ=0 (The mean prediction error is equal to zero.)H1:...

Q: How do I solve question 1 and 2?

A: From the given question,

Q: Uncertainty True or false: If correct methods of hypothesis testing are used with a large simple ran...

A: Click to see the answer

Q: Regarding the criterion used to decide on the plane that best fits a set of data points in k + 1 dim...

A: a)Least-square criterion:The least-square criterion is the criterion using which it is determined th...

Q: P-Value Find the P-value in a test of the claim that the mean annual income of a CIA agent is greate...

A: The P-value is calculated by using Excel:The degrees of freedom is n-1 which is equal to 39.

Q: For a t-curve with df = 18, obtain the t-value and illustrate your results graphically. a. The t-val...

A: The given results can be obtained by using MINITAB.a).Step-by-step procedure to obtain probability d...

Q: Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and tes...

A: Click to see the answer

Q: Car Fatalities The recent rate of car fatalities was 33,561 fatalities for 2969 billion miles travel...

A: GivenThe recent rate of car fatalities was 33,561 fatalities for 2969 billion miles traveled.Mean = ...

Q: Regarding the estimate of the conditional standard deviation,s,, which of the three sums of squares ...

A: Estimate of the conditional standard deviation:

Q: Regarding the regression of a response variable, y, on predictor variable, x, what is meant by strai...

A: Straightening the scatterplot:To fit a simple linear regression line, the data set of the predictor ...

Q: A researcher brings a sample of political activists into their laboratory. Each activist is shown on...

A: From the given information, each activist is shown one video for Candidate A and separate video for ...

Q: A variable of two populations has a mean of 40 and a standard deviation of 12 for one of the populat...

A: a.The mean of x1 and x2  is,

Q: Quality Control After constructing a new manufacturing machine, five prototype integrated circuit ch...

A: a. From given information, there are five prototype integrated circuit chips. In five chips, two are...