Consider the following data: x 4 5 6 7 8 P(X=x) 0.2 0.2 0.1 0.2 0.3

Step 2 of 5: Find the variance. Round your answer to one decimal place.

Step 3 of 5: Find the standard deviation. Round your answer to one decimal place.

Step 4 of 5: Find the value of P(X<7). Round your answer to one decimal place

Step 5 of 5:Find the value of P(X≥7). Round your answer to one decimal place.

A data set about speed dating includes​ "like" ratings of male dates made by the female dates. The summary statistics are

nequals=193193​,

x overbarxequals=7.867.86​,

sequals=2.262.26.

Use a

0.100.10

significance level to test the claim that the population mean of such ratings is less than

8.008.00.

Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

The authors of a paper describe an experiment to evaluate the effect of using a cell phone on reaction time. Subjects were asked to perform a simulated driving task while talking on a cell phone. While performing this task, occasional red and green lights flashed on the computer screen. If a green light flashed, subjects were to continue driving, but if a red light flashed, subjects were to brake as quickly as possible. The reaction time (in msec) was recorded. The following summary statistics are based on a graph that appeared in the paper. n = 61 x = 530 s = 75 (a) Assuming that this sample is random/representative of the population, what other assumptions need to be true before we can create a confidence interval? Yes, because the population distribution is normal. No, because n < 30 No, because either np̂ < 10 or n(1−p̂) < 10 Yes, because np̂ ≥ 10 and n(1−p̂)≥ 10 Yes, because n ≥ 30 No, because the population distribution is not normal. Changed: Your submitted answer was incorrect. Your current answer has not been submitted. (b) Construct a 98% confidence interval for μ, the mean time to react to a red light while talking on a cell phone. (Round your answers to three decimal places.) , (c) Interpret a 98% confidence interval for μ, the mean time to react to a red light while talking on a cell phone. We are % confident that the mean time to react to a is between and milliseconds. (d) Suppose that the researchers wanted to estimate the mean reaction time to within 5 msec with 95% confidence. Using the sample standard deviation from the study described as a preliminary estimate of the standard deviation of reaction times, compute the required sample size. (Round your answer up to the nearest whole number.) n = You may need to use the appropriate table in Appendix A to answer this question.

A claimed trend of thinner Miss America winners has generated charges that the contest encourages unhealthy diet habits among young women. Listed below are body mass indexes (BMI) for recent Miss America winners. Use a 0.01 significance level to test the claim that recent winners are from a population with a mean BMI less than 18.5, which is considered underweight. Assume that the sample has been randomly selected from a population with a normal distribution. 19.5 20.3 19.6 20.2 17.8 17.9 19.1 18.8 17.6 16.8

Audrey and Diana go fishing at the Lyndon Fishing Pond. Upon arrival the owner informs them that the pond is stocked with an infinite number of independent fish, and that a typical fisher catches fish at a Poisson rate of 2 fish per hour. There are 10 other people fishing there that day. Diana has the same skill level as a typical fisher but Audrey catches on average twice as many fish as a typical fisher.

(a) (2) Find the mean and variance of the total number of fish caught over 5 hours.

For the rest of the question, assume that 90 fish were caught that day.
(b) (3) Show that we have the following probabilities. Use those rounded probabilities in parts b), c) and d):
i. The probability a fish was caught by Audrey is 0.154
ii. The probability a fish was caught by Diana is 0.077
iii. The probability a fish was caught by someone else is 0.769

(c) (2) Find the probability that Audrey catches 15 fish and Diana catches 15 fish

(d) (2) Find the probability that Audrey and Diana catch 30 fish together

(e) (2) Given that Audrey catches 15 fish, find the probability that Diana catches 15 fish

(f) (2) Explain logically the difference between the probabilities in (c), (d), and (e)

Car manufacturers are interested in whether there is a relationship between the size of car an individual drives and the number of people in the driver's family (that is, whether car size and family size are independent). To test this, suppose that 797 car owners were randomly surveyed with the following results. Conduct a test for independence at the 5% level.

A. What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)

B. State the distribution to use for the test.

C. What is the test statistic? (Round your answer to two decimal places.)

D. What is the p-value? (Round your answer to four decimal places.)

E. Alpha (Enter an exact number as an integer, fraction, or decimal.)
α =

μ = the population mean speed (mph) of trucks in a specific region in Greeley, CO. A random sample of 8 trucks has a sample mean speed of 25.4 mph and the population standard deviation is known to be 3.2 mph. Find the 95% confidence interval for μ.

a.) (23.18, 27.62)

b.) (12.68, 18.70)

c.) (24.08, 30.05)

d.) (18.80, 24.56)

What is the required sample size if you want an error margin for the 95% confidence interval for μ to equal 0.8 mph?

a.) 62

b.) 60

c.) 58

d.) 64

The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.01 level that the drug stays in the system for more than 340 minutes. For a sample of 49 patients, the mean time the drug stayed in the system was 346 minutes. Assume the population standard deviation is 18. State the alternative and null hypotheses.

For this problem, we want to compare the delivery speed between Company A and Company B, The question being answered is whether there is a significant difference in the average cycle time to deliver a from Company A vs. Company B.

Null Hypothesis?

Alternative Hypothesis?

One tail or Two tails?

Are these independent samples?

Use Excel if you can

La Leche League International reports that the mean age of weaning a child from breastfeeding is age four to five worldwide. In America, most nursing mothers wean their children much earlier. Suppose a random survey is conducted of 21 U.S. mothers who recently weaned their children. The mean weaning age was 9 months (3/4 year) with a standard deviation of 3 months. Conduct a hypothesis test to determine if the mean weaning age in the U.S. is less than four years old. Conduct a hypothesis test at the 5% level. Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) A.) State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom.) B.) What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.) C.) What is the p-value? (Round your answer to four decimal places.) D.) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) E.) Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Enter your answers in years. Round your answers to four decimal places.)

A survey was conducted that asked 1014 people how many books they had read in the past year. Results indicated that x over bar x equals=13.6 books and s equals=16.6 books. Construct a 95​% confidence interval for the mean number of books people read. Interpret the interval. Construct a 95​% confidence interval for the mean number of books people read and interpret the result. Select the correct choice below and fill in the answer boxes to complete your choice.

​(Use ascending order. Round to two decimal places as​ needed.)

A.There is 95​% confidence that the population mean number of books read is between ? and ?.

B.There is a 95​% chance that the true mean number of books read is between ? and ?.

C.If repeated samples are​ taken,95​% of them will have a sample mean between ? and ?.

Since an instant replay system for tennis was introduced at a major​ tournament, men challenged 13861386 referee​ calls, with the result that 427427 of the calls were overturned. Women challenged 763763 referee​ calls, and 224224 of the calls were overturned. Use a 0.010.01 significance level to test the claim that men and women have equal success in challenging calls. Complete parts​ (a) through​ (c) below. a. Test the claim using a hypothesis test. Consider the first sample to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female tennis players who challenged referee calls. What are the null and alternative hypotheses for the hypothesis​ test? A. Upper H 0H0​: p 1p1equals=p 2p2 Upper H 1H1​: p 1p1less than

p 2p2 E. Upper H 0H0​: p 1p1greater than or equals≥p 2p2 Upper H 1H1​: p 1p1not equals≠p 2p2 F. Upper H 0H0​: p 1p1not equals≠p 2p2 Upper H 1H1​: p 1p1equals=p 2p2 Identify the test statistic. zequals=nothing ​(Round to two decimal places as​ needed.) Identify the​ P-value. ​P-valueequals=nothing ​(Round to three decimal places as​ needed.) What is the conclusion based on the hypothesis​ test? The​ P-value is ▼ greater than less than the significance level of alphaαequals=0.010.01​, so ▼ fail to reject reject the null hypothesis. There ▼ is not sufficient is sufficient evidence to warrant rejection of the claim that women and men have equal success in challenging calls. b. Test the claim by constructing an appropriate confidence interval. The 9999​% confidence interval is nothingless than

1. (a) If A and B are independent events with P(A) = 0.6 and P(B) = 0.7, find P (A or B).

(b) A randomly selected student takes Biology or Math with probability 0.8, takes Biology and Math with probability 0.3, and takes Biology with probability 0.5. Find the probability of taking Math.

2. A box contains 4 blue, 6 red and 8 green chips.

1. In how many different ways can you select 2 blue, 3 red and 5 green chips? (Give the exact numerical value).

2. Draw two chips in a row without replacement. Find the probability that both chips are green.

3. Based on the following table, compute the probabilities below:

P (Women and Yes) =

P (Men | Yes) =

P (No | Women) =

P (Men or No) =

Are Men and No Opinion mutually exclusive?

Are Men and No Opinion independent? Justify your answer by an appropriate computation.

With the diagrams please

4. The Federal Reserve reports that the mean lifespan of a five dollar bill is 4.9 years.   Let’s suppose that the standard deviation is 2.1 years and that the distribution of lifespans is normal (not unreasonable!)

Find: (a) the probability that a $5 bill will last more than 4 years.

(b) the probability that a $5 bill will last between 5 and 7 years.

(c) the 94^th percentile for the lifespan of these bills (a time such that 94% of bills last less than that time).

(d ) the probability that a random sample of 37 bills has a mean lifespan of more than 5.1 years.

DON'T FORGET THE DIAGRAMS, PLEASE

Life rating in Greece. Greece faced a severe economic crisis since the end of 2009. Suppose a Gallup poll surveyed 1,000 randomly sampled Greeks in 2011 and found that 27% of them said they would rate their lives poorly enough to be considered "suffering." Round all answers to four decimal places. 1. What is the population parameter of interest? A. The 25% of Greeks in the sample who believe they are suffering. B. The actual proportion of Greeks who believe they are suffering. C. The score on the survey that corresponds to suffering. D. All the people who live in Greece. 2. What is the value of the point estimate of this parameter? 3. Construct a 95% confidence interval for the proportion of Greeks who are "suffering." ( , ) 4. If we decided to use a higher confidence level, the confidence interval would be: A. wider B. narrower C. stay the same 5. If we used the same confidence level with a larger sample, the confidence interval would be: A. wider B. narrower C. stay the same