You wish to test the following claim (H1H1) at a significance level of α=0.10α=0.10. For the context of this problem, d=x2−x1d=x2-x1 where the first data set represents a pre-test and the second data set represents a post-test.

      Ho:μd=0Ho:μd=0
      H1:μd≠0H1:μd≠0

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = ±±

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

• in the critical region
• not in the critical region

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.
• There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.
• The sample data support the claim that the mean difference of post-test from pre-test is not equal to 0.
• There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is not equal to 0.

You wish to test the following claim (H1H1) at a significance level of α=0.005α=0.005.

      Ho:p1=p2Ho:p1=p2
      H1:p1>p2H1:p1>p2

You obtain a sample from the first population with 334 successes and 359 failures. You obtain a sample from the second population with 240 successes and 359 failures.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion.
• There is not sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion.
• The sample data support the claim that the first population proportion is greater than the second population proportion.
• There is not sufficient sample evidence to support the claim that the first population proportion is greater than the second population proportion.

I got the following equation from the lesson's summary:

P(X=k) = (e^-µ  µ^K) / k!

When calculating the probability while answering the homework problems I always seemed to be off by a very small amount. The only explanation given under the problem after hitting show answer is 1 - P(x=0) -P(x=1) - ... up until x = the number given in the question. I am confused where this equation or these types of calculations are coming from and would love some help!

Suppose that a random sample of size 64 is to be selected from a population with mean 40 and standard deviation 5.

a) What is the approximate probability that x will differ from μ by more than 0.8? (Round your answer to four decimal places.)

In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. Furthermore, there is a weight limit of 2500 lb. Assume that the average weight of students, faculty, and staff on campus is 154 lb, that the standard deviation is 27 lb, and that the distribution of weights of individuals on campus is approximately normal. If a random sample of 16 persons from the campus is to be taken:

What is the expected value of the sample mean of their weights?
μ_x =  lb

(b) What is the standard deviation of the sampling distribution of the sample mean weight? (Round your answer to two decimal places.)
σ_x =  lb

(c) What average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 lb? (Round your answer to two decimal places.)
x >  lb

(d) What is the chance that a random sample of 16 persons on the elevator will exceed the weight limit? (Round your answer to four decimal places.)
P =

Detail the steps in computing the One-Way Anova with a brief discussion specific to the important aspects of each step.

1. A professor using an open source introductory statistics book predicts that 10% of the students will purchase a hard copy of the book, 55% will print it out from the web, and 35% will read it online. At the end of the semester he asks his students to complete a survey where they indicate what format of the book they used. Of the 200 students, 25 said they bought a hard copy of the book, 85 said they printed it out from the web, and 90 said they read it online.

(a) State the hypotheses for testing if the professor's predictions were inaccurate.

• Ho: p_Buy = .1, p_Print=.55, p_Online=.35
  Ha: at least one of the claimed probabilities is different
• Ho: p_Buy = .1, p_Print=.55, p_Online=.35
  Ha: all of the claimed probabilities are different
• Ho: p_Buy = .1, p_Print=.55, p_Online=.35
  Ha: at least one of the claimed probabilities is zero

(b) How many students did the professor expect to buy the book, print the book, and read the book exclusively online? (if necessary, round to the nearest whole number)

(c) Calculate the chi-squared statistic, the degrees of freedom associated with it, and the p-value.

The value of the test-statistic is:  (please round to two decimal places)

The degrees of freedom associated with this test are:

The p-value associated with this test is:

• greater than .1
• less than .01
• between .05 and .1
• between .01 and .05

(e) Based on the p-value calculated in part (d), what is the conclusion of the hypothesis test?

• Since p ≥ α we reject the null hypothesis and accept the alternative
• Since p<α we reject the null hypothesis and accept the alternative
• Since p ≥ α we do not have enough evidence to reject the null hypothesis
• Since p<α we fail to reject the null hypothesis
• Since p ≥ α we accept the null hypothesis

Interpret your conclusion in this context.

• The data provide sufficient evidence to claim that the actual distribution differs from what the professor expected
• The data do not provide sufficient evidence to claim that the actual distribution differs from what the professor expected

If we define a convenient unit (convenient unit for monitoring chart) = 100 boards and the sample size is n = 2.5.

(a) How many boards should be checked at each sampling time?

(b) Assume in control Phase I data, we found 50 defects in 1000 boards, what are the estimated ?₀ and ?₀?

(c) What are the CL, UCL/LCL for the c and u charts based on (b)?

(d) If at the sampling time t, 13 defects are found in a sample, what is the monitoring statistic value to be plotted in the c chart and u chart?

(e) Continue (d), which monitoring statistic follows the Poisson distribution? What is the Poisson distribution parameter?

Imagine that a group of obese children is recruited for a study in which their weight is measured, then they participate for 3 months in a program that encourages them to be more active, and finally their weight is measured again.

Explain how each of the following might affect the results:

regression to the mean

spontaneous remission

history

maturation

al least 350words

Workers and​ senior-level bosses were asked if it was seriously unethical to monitor employee​ e-mail. The results are summarized in the table to the right. Use a 0.05 significance level to test the claim that the response is independent of whether the subject is a worker or a boss. Yes No Workers 200 200 250 250 Bosses 36 36 81 81 a. State the null and the alternative hypotheses. Choose the correct answer below. A. The null​ hypothesis: Response is independent of whether the subject is a worker or a​ senior-level boss. The alternative​ hypothesis: There is some relationship between response and whether the subject is a worker or a​ senior-level boss. Your answer is correct. B. The null​ hypothesis: There is some relationship between response and whether the subject is a worker or a​ senior-level boss. The alternative​ hypothesis: Response is independent of whether the subject is a worker or a​ senior-level boss. b. Assuming independence between the two​ variables, find the expected frequency for each cell of the table. Table of expected frequencies Yes No Workers 187.3 187.3 262.7 262.7 Bosses 48.7 48.7 68.3 68.3 ​(Round to the nearest tenth as​ needed.) c. Find the value of the chi squared χ2 test statistic. chi squared χ2 equals = nothing ​(Round to the nearest hundredth as​ needed.)

The amount of time a bank teller spends with each customer has a population​ mean, mu​, of 2.80 minutes and a standard​ deviation, sigma​, of 0.40 minute. Complete parts​ (a) through​ (d).

d.) If you select a random sample of 64 customers, there is an 83​% chance that the sample mean is less than how many​ minutes?

In a large corporation, 65% of the employees are male. A random sample of 5 employees is selected. We wish to determine the probability of selecting exactly 3 males. Use an appropriate probability distribution to answer the following:

(a) Define the variable of interest for this scenario.

(b) What is the probability that the sample contains exactly three male employees?

(c) Justify the suitability of the probability distribution that you used to solve part (a).

(d) What is the expected number of male employees in the sample?

Consider the following sets of sample data: A: $30,600, $29,900, $37,500, $29,200, $25,100, $37,400, $26,100, $35,400, $31,500, $34,600, $33,200, $23,100, $25,200, $38,000

B: 89, 78, 85, 81, 76, 97, 70, 73, 88, 76, 99

Step 1 of 2: For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.

CV FOR DATA SET A:

CV FOR DATA SET B:

Step 2 of 2:

Which of the above sets of sample data has the smaller spread?

Exit polling is a popular technique used to determine the outcome of an election prior to results being tallied. Suppose a referendum to increase funding for education is on the ballot in a large town​ (voting population over​ 100,000). An exit poll of 300 voters finds that 156 voted for the referendum. How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.49​? Based on your​ result, comment on the dangers of using exit polling to call elections. How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.49​? The probability that more than 156 people voted for the referendum is nothing. ​(Round to four decimal places as​ needed.) Comment on the dangers of using exit polling to call elections. Choose the correct answer below. A. The result is unusual because the probability that ModifyingAbove p with caret is equal to or more extreme than the sample proportion is greater than​ 5%. Thus, it is not unusual for a wrong call to be made in an election if exit polling alone is considered. B. The result is not unusual because the probability that ModifyingAbove p with caret is equal to or more extreme than the sample proportion is greater than​ 5%. Thus, it is not unusual for a wrong call to be made in an election if exit polling alone is considered. C. The result is unusual because the probability that ModifyingAbove p with caret is equal to or more extreme than the sample proportion is less than​ 5%. Thus, it is unusual for a wrong call to be made in an election if exit polling alone is considered. D. The result is not unusual because the probability that ModifyingAbove p with caret is equal to or more extreme than the sample proportion is less than​ 5%. Thus, it is unusual for a wrong call to be made in an election if exit polling alone is considered.

1. Let Y be a uniformly distribution random variable. Find:

   (a) P(|Y −μ|≤2σ)
   (b) Use Tchebysheff’s theorem to estimate P(|Y − μ| ≤ 2σ).
   (c) Use the empirical rule to estimate P (|Y − μ| ≤ 2σ).
   (d) How does (b) compare to (a)?
   (e) How does (c) compare to (a)?