Problems 16-18: Lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.(Use the z-table). What percentage of pregnancies last less than 250 days?

What percentage of pregnancies last more than 280 days?

If 60 pregnant women were randomly selected, how likely is it that their mean pregnancy length is greater than 275 days? Your answer:

A fishing lake camp boasts that about 30% of the guests catch lake trout over 20 pounds on a 4-day fishing trip. Let n be a random variable that represents the first trip to the camp on which a guest catches a lake trout over 20 pounds.

(a) Write out a formula for the probability distribution of the random variable n.
P(n) =

(b) Find the probability that a guest catches a lake trout weighing at least 20 pounds for the first time on trip number 3. (Round your answer to three decimal places.)


(c) Find the probability that it takes more than three trips for a guest to catch a lake trout weighing at least 20 pounds. (Round your answer to three decimal places.)


(d) What is the expected number of fishing trips that must be taken to catch the first lake trout over 20 pounds? Hint: Use μ for the geometric distribution and round. (Round your answer to two decimal places.)
(    ) trips

Please Use your keyboard (Don't use handwriting)

Stat

(1)

An insurance company believes that people can be divided into two classes: those who are an accident prone and those who are not. The company’s statistics show that an accident-prone person will have an accident at some time within a fixed 1-year period with probability .4, whereas this probability decreases to .2 for a person who is not accident-prone.
(i) If we assume that 30 percent of the population is accident prone, what is the probability that a new policyholder will have an accident within a year of purchasing a policy?
(ii) Suppose that a new policyholder has an accident within a year of purchasing a policy. What is the probability that he or she is accident-prone?

(2)

Two boxes containing marbles are placed on a table. The boxes are labeled B1 and B2. Box B1 contains 7 green marbles and 4 white marbles. Box B2 contains 3 green marbles and 10 yellow marbles. The boxes are arranged so that the probability of selecting box B1 is 1/3 and the probability of selecting box B2 is 2/3 FATIMAH is blindfolded and asked to select 3 marbles. She will win a color TV if she selects a green marble.
(i) What is the probability that FATIMAH will win the TV (that is, she will select a green marble)?
(ii) If FATIMAH wins the color TV, what is the probability that the green marble was selected from the first box?

(3)

One-half percent of the population has CORONA Virus. There is a test to detect CORONA. A positive test result is supposed to mean that you have CORONA but the test is not perfect. For people with CORONA, the test misses the diagnosis 2% of the times. And for the people without CORONA, the test incorrectly tells 3% of them that they have CORONA.
(i) What is the probability that a person picked at random will test positive?
(ii) What is the probability that you have CORONA given that your test comes back positive?

(4)

A device is composed of two components, A and B, subject to random failures. The components are connected in parallel and, consequently, the device is down only if both components are down. The two components are not independent. We estimate that the probability of:
a failure of component A is equal to 0.2;
a failure of component B is equal to 0.8 if component A is down;
a failure of component B is equal to 0.4 if component A is active.
(a)

Calculate the probability of a failure
(i) of component A if component B is down
(ii) of exactly one component
(b)

In order to increase the reliability of the device, a third component, C, is added in such a way that components A, B, and C are connected in parallel. The probability that component C breaks down is equal to 0.2, independently of the state (up or down) of components A and B. Given that the device is active, what is the
probability that component C is down?

A television station wishes to study the relationship between viewership of its 11 p.m. news program and viewer age (18 years or less, 19 to 35, 36 to 54, 55 or older). A sample of 250 television viewers in each age group is randomly selected, and the number who watch the station’s 11 p.m. news is found for each sample. The results are given in the table below.

(a) Let p₁, p₂, p₃, and p₄ be the proportions of all viewers in each age group who watch the station’s 11 p.m. news. If these proportions are equal, then whether a viewer watches the station’s 11 p.m. news is independent of the viewer’s age group. Therefore, we can test the null hypothesis H₀ that p₁, p₂, p₃, and p₄ are equal by carrying out a chi-square test for independence. Perform this test by setting α = .05. (Round your answer to 3 decimal places.)

χ2χ2 =            

so (Click to select)Do not rejectReject H₀: independence

(b) Compute a 95 percent confidence interval for the difference between p₁ and p₄. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

95% CI: [  , ]

You may need to use the appropriate appendix table or technology to answer this question. A binomial probability distribution has p = 0.20 and n = 100. (a) What are the mean and standard deviation?

)

What is the probability of exactly 24 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(d)

What is the probability of 16 to 24 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(e)

What is the probability of 15 or fewer successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

1) You wonder whether men or women are more likely to be driving when both a man and a woman are in the front seat of a car. You observe 20 cars with both a man and a woman in the front seat and count how many times the man is driving. Of the 20 cars you observed, the man was driving in 15 of them.

What is the probability value for this result? (Give your answer to at least 3 places past the decimal point)

Selected Answer: 2.24

Response Feedback: Incorrect, Review Chapter 11, the Logic of Hypothesis Testing Note that you will need to use Excel or the binomial calculator for this problem http://onlinestatbook.com/2/java/binomialProb.html Note that this is a 2-tailed test because you asked whether men or women were more likely to be driving. Make sure you include both tails.

data for the selling prices of homes in a ZIP code and the square footage of those homes. Use the Spearman rank correlation to determine if there is a significant correlation between the home price and the square footage.

The current median survival time of patients  with acute myelogenous lukemia who achieve complete remission from conventional treatment is 21 months. A new procedure is being studied. Researchers hoped that with this new procedure, the median survival time will be improved. The following is the survival time for 10 patients who received the new treatment:

Patient: 1,2,3,4,5,6,7,8,9,10

Survival Time: 24.1, 25.8, 20.5, 20.9, 27.3, 21.5, 20.1, 28.9, 19.2, 26.3

A) Let M be the median survival time for patients under the new treatment. What is the appropriate alternative hypothesis?

B) Find the p-value of the Sign Test for the appropriate hypotheses.

C) Find the value of the Wilcoxon Signed-Rank test statistic for the appropriate hypotheses

A study of iron deficiency among infants compared samples of infants following different feeding regimens. One group contained breast-fed infants, while the infants in another group were fed a standard baby formula without any iron supplements. Here are summary results on blood hemoglobin levels at 12 months of age.

Group n x s

Breast-fed 22 13.3 1.7

Formula 18 12.4 1.8

(a) Is there significant evidence that the mean hemoglobin level is higher among breast-fed babies? State H0 and Ha.

H0: μbreast-fed = μformula; Ha: μbreast-fed > μformula

H0: μbreast-fed < μformula; Ha: μbreast-fed = μformula

H0: μbreast-fed > μformula; Ha: μbreast-fed = μformula

H0: μbreast-fed ≠ μformula; Ha: μbreast-fed < μformula

Carry out a t test. Give the P-value. (Use α = 0.01. Use μbreast-fed − μformula. Round your value for t to three decimal places, and round your P-value to four decimal places.)

t =

P-value =

What is your conclusion?

Reject the null hypothesis. There is significant evidence that the mean hemoglobin level is higher among breast-fed babies.

Reject the null hypothesis. There is not significant evidence that the mean hemoglobin level is higher among breast-fed babies.

Fail to reject the null hypothesis. There is significant evidence that the mean hemoglobin level is higher among breast-fed babies.

Fail to reject the null hypothesis. There is not significant evidence that the mean hemoglobin level is higher among breast-fed babies.

(b) Give a 95% confidence interval for the mean difference in hemoglobin level between the two populations of infants. (Round your answers to three decimal places.) ,

(c) State the assumptions that your procedures in (a) and (b) require in order to be valid.

We need sample sizes greater than 40.

We need the data to be from a skewed distribution.

We need two independent SRSs from normal populations.

We need two dependent SRSs from normal populations.

A test for a certain drug produces a false negative 3% of the time and a false positive 9% of the time. Suppose 12% of the employees at a certain company use the drug. If an employee at the company tests negative, what is the probability that he or she does use the drug?

Let y1, y2, .....y10 be a random sample from an exponential pdf with unknown parameter λ. Find the form of the GLRT for H0: λ=λ0 versus H1:λ ≠ λ0. What integral would have to be evaluated to determine the critical value if α were equal to 0.05?

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x overbar​, is found to be 112​, and the sample standard​ deviation, s, is found to be 10. ​(a) Construct a 95​% confidence interval about mu if the sample​ size, n, is 23. ​(b) Construct a 95​% confidence interval about mu if the sample​ size, n, is 16. ​(c) Construct a 90​% confidence interval about mu if the sample​ size, n, is 23. ​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed?

For a particular chemical synthesis, the effect of precursor concentration and catalyst amount were studied.

Calculate the : a)effect of each factor and interaction between factors, b)significance of each factor and interactions, c) residuals between the actual value and the linear statistical model based on the estimates from 1. Do you think the residuals are normally distributed.

An adoption agency compared the cost of the adopting babies from China and Russia (for people living in the US). The average cost of adopting a baby from China was $11,045 with a sample standard deviation of $535. The average cost of adopting a baby from Russia was $10,800 with a sample standard deviation of $550. These data were gathered from two samples of 30 each. Assume the variances of the two samples are UNEQUAL. (1 pt.) Write out Ho and Ha to test if the average costs are different for the two countries. (1 pt.) calculate the p-value and attach your output sheet printout. (1 pt.) Can we reject Ho at the 95% confidence level? . Can we be 95% confident that costs of adoption are different for the two countries?