A trucking company wants to find out if their drivers are still alert after driving long hours. So, they give a test for alertness to two groups of drivers. They give the test to 400 drivers who have just finished driving 4 hours or less and they give the test to 585 drivers who have just finished driving 8 hours or more. The results of the tests are given below.

Passed Failed
Drove 4 hours or less 310 90
Drove 8 hours or more 415 170

Is there is a relationship between hours of driving and alertness? (Do a test for independence.) Test at the 1 % level of significance.

Case studies showed that out of 10,409 convicts who escaped from certain prisons, only 7958 were recaptured.

(a) Let p represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)

A simple random sample of checks were categorized based on the number of cents on the written check and recorded below. Cents Category 0¢-24¢ 25¢-49¢ 50¢-74¢ 75¢-99¢ Frequency 58 37 28 17 Use the p-value method and a 5% significance level to test the claim that 50% of the check population falls into the 0¢-24¢ category, 20% of the check population falls into the 25¢-49¢ category, 16% of the check population falls into the 50¢-74¢ category, and 14% of the check population falls into the 75¢-99¢ category. Calculate the expected value for the 50¢-74¢ category (round to the nearest tenth).

The United States Centers for Disease Control and Prevention (CDC) found that 17.9%17.9% of women ages 1212–5959 test seropositive for HPV‑16. Suppose that Tara, an infectious disease specialist, assays blood serum from a random sample of n=1000n=1000 women in the United States aged 1212–59.59.

Apply the central limit theorem for the distribution of a sample proportion to find the probability that the proportion, ^p,p^, of women in Tara's sample who test positive for HPV‑16 is greater than 0.1990.199. Express the result as a decimal precise to three places.

P(^p>0.199)=

Apply the central limit theorem for the distribution of a sample proportion to find the probability that the proportion of women in Tara's sample who test positive for HPV‑16 is less than 0.1740.174. Express the result as a decimal precise to three places.

P(^p<0.174)=

(Please answer this question accuratelly THANKS)

The following commands in R computes 5000 simulations of sample means of size 12 from a normal distribution with mean µ = 100 and standard deviation σ = 14. require

(fastR2) nsamplesum <- do(5000) * c(sample.mean=mean(rnorm(12,100,14)))

The following commands compute the approximate mean and standard deviation of the sample mean and plot the histogram giving the approximate distribution of the sample mean.

mean(∼ sample.mean, data=nsamplesum) sd(∼ sample.mean, data=nsamplesum) gf dhistogram(∼ sample.mean, data= nsamplesum, bins=20)

(a) Compare the approximate values of mean and standard deviation of the sample mean found above with the expected theoretical ones.

(b) Repeat the same simulation as above using now samples from a uniform distribution in the interval [−2, 4]. Also in this case, run a numerical test over 5000 simulations, compute mean and standard deviation of the sample mean, and compare it to the theoretical result.

Compare the kk-NN classifier, linear discriminant analysis (LDA) and the logistic model when it comes to classification. Which is generally better?

26. A sample of 1100 computer chips revealed that 62% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 60% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage. State the null and alternative hypotheses.

H0:

Ha:

27. A sample of 1100 computer chips revealed that 62% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 60% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage. Make the decision to reject or fail to reject the null hypothesis at the 0.10 level.

An article suggested that yield strength (ksi) for A36 grade steel is normally distributed with μ = 45 and σ = 4.5.

(a) What is the probability that yield strength is at most 40? Greater than 63? (Round your answers to four decimal places.)

(b) What yield strength value separates the strongest 75% from the others? (Round your answer to three decimal places.)
ksi

A study of long-distance phone calls made from the corporate offices of the Pepsi Bottling Group Inc. showed the calls follow the normal distribution. The mean length of time per call was 4.2 minutes and the standard deviation was 0.60 minutes

a) What is the probability the calls lasted between 3.5 and 4.1 minutes?

b) What is the probability the calls lasted less than 3.4 minutes?

c) As part of her report to the president, the director of communications would like to report the minimum length of the longest (in duration) 4% of the calls. What is this time?

d) As part of her report to the president, the director of communications would like to report the maximum length of the shortest (in duration) 8% of the calls. What is this time?

Suppose we wish to test the hypothesis H0 :μ=45vs. H1 :μ>45.

What will be the result if we conclude that the mean is 45 when the actual mean is 50? Choose one of the following.

1. We have made a Type I error.
2. We have made a Type II error.
3. We have made the correct decision.

1. Use t and F to test for a significant relationship between HRS1 and age. Use α = 0.05 and make sure you know what hypotheses you are using to conduct the significance tests.
2. Calculate and interpret the coefficient of determination R². Based on this R², did the estimated regression equation provide a good fit? Briefly justify your answer. Hint: If you used Excel Regression Tool to answer part c, R² was reported with your output.
3. Use the estimated regression equation to predict the HRS1 for a 60 year old individual.

Please show work in Excel thank you

Problem Scenario: Following is a problem description. For all hypothesis tests, you MUST state the statistical test you are using and use the P-VALUE METHOD through Microsoft Excel to make your decision. Show all steps, calculations, and work. For confidence intervals there is a specific Excel tool for each interval.  Treat each part of the question as a separate problem -- we use the same data set but are answering different “research questions”.

Many parts of cars are mechanically tested to be certain that they do not fail prematurely. In an experiment to determine which one of two types of metal alloy produces superior door hinges, 40 of each type were tested until they failed. To evaluate how long hinges made with the different alloys would last, the number of openings and closings was observed and recorded (to the closest 0.1 million). Car manufacturers consider any hinge that does not survive 1 million openings and closings to be a failure., A statistician has determined that the number of openings and closings is normally distributed.

NOTE: use ONLY the P-value method for hypothesis tests.

Number of Openings and Closings

a.) Estimate with 90% confidence the difference in the number of openings and closings between hinges made with Alloy1 and hinges made with Alloy 2. Interpret the interval.

b.) The quality control manager is not only concerned about the openings and closings of the hinges but is also concerned about the proportion of hinges that fail. Can we infer at the 10% significance level that the proportion of hinges made with Alloy 2 that fail exceeds 18%?

1.A large government building has received a telephone call threatening that an explosive device has been placed somewhere in the building. The bomb squad has been called to check out the threat and they have ordered all occupants to leave the building. The bomb squad will check out the building and declare whether or not it is safe to renter. (a) State the null and alternate hypothesis that is facing the bomb squad. (b) state the type-I and type-II error in this situation (c) which error is more serious here and why?  

2. A manufacturer of drinking water filters claims that their cartridge last more than 300 liters before they have to be replaced. A consumer group wants to confirm this claim and selects a random sample of 60 cartridges for testing. The cartridges produce a sample average lifetime of 312 liters, and a sample standard deviation of 50 liters. Construct a null and alternate hypothesis that the consumer group should use to confirm the manufacturer’s claim. Based on the sample data, what can the group conclude? Use a 5% level of significance. Would your answer change if you used a 1% level of significance? Justify

Two fair dice are rolled and the outcomes are recorded. Let X denotes the larger of the two numbers obtained and Y the smaller of the two numbers obtained. Determine probability mass functions for X and Y, and the cumulative distribution functions for X and for Y. Present the two cumulative distribution functions in a plot. Calculate E (2X + 2Y −8).

According to a social media​ blog, time spent on a certain social networking website has a mean of 22 minutes per visit. Assume that time spent on the social networking site per visit is normally distributed and that the standard deviation is 7 minutes. Complete parts​ (a) through​ (d) below.

a. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 21.5 and 22.5 ​minutes? ___ ​(Round to three decimal places as​ needed.)

b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 21 and 22 minutes? ___ ​(Round to three decimal places as​ needed.)

c. If you select a random sample of 144 ​sessions, what is the probability that the sample mean is between 15.5 and 16.5 ​minutes? ​____ (Round to three decimal places as​ needed.)

d. Explain the difference in the results of​ (a) and​ (c).

The sample size in​ (c) is greater than the sample size in​ (a), so the standard error of the mean​ (or the standard deviation of the sampling​ distribution) in​ (c) is

______ than in​ (a). As the standard error _______ values become more concentrated around the mean.​ Therefore, the probability that the sample mean will fall in a region that includes the population mean will always ______ when the sample size increases.