Statistics and Probability Answers

A coin tossed and die is rolled. The outcome of the coin is recoded "1" when it shows a head, and "0" when it shows a tail. The random variable gives the sum of the outcomes of coin and die. Compute the average value of the random variable?

A coin tossed and die is rolled. The outcome of the coin is recoded "1" when it shows a head, and "0" when it shows a tail. The random variable gives the sum of the outcomes of coin and die. Compute the average value of the random variable?

 A population consists of four members {3, 8, 10, 15}. Consider all possible samples of size 2 that can be drawn with replacement from the population

The mean I.Q of a sample of 1600 children was 99. It is likely that this was a random sample from a population with mean I.Q 100 and standard deviation 15.

 Required:

Using appropriate statistics, deduce whether there is any statistically significant difference between the two means if z critical value at α = .05 is 1.96        

There are 12 movies showing at a theater. Four are action movies, two are children's movies and the other movies are comedies. Kevin randomly selects 2 different movies to see. He will not see a movie twice. What is the probability that the 1st movie is an action movie and the second movie is a comedy?

Unit 5 deals with two types of discrete random variables, the Binomial and the Poisson, and two types of continuous random variables, the Uniform and the Exponential. Depending on the context, these types of random variables may serve as theoretical models of the uncertainty associated with the outcome of a measurement.

Give an example, USING YOUR OWN WORDS, of how either the Poisson or the Exponential distribution could be used to model something in real life. You can give an example in an area that interests you (a list of ideas is below). Give a very rough description of the sample space.

If you use an idea from another source, please provide a citation in the sentence and a reference entry at the end of your post. Include a citation even if you paraphrase from a website. Please do not copy blocks of text from the Internet--try to use your own words.

When forming your answer to this question you may give an example of a situation from your own field of interest for which a random variable, possibly from one of the types that are presented in this unit, can serve as a model. Discuss the importance (or lack thereof) of having a theoretical model for the situation. People can use models to predict business conditions, network traffic levels, sales, number of customers per day, rainfall, temperature, crime rates, or other such things.

TRUE OR FALSE

1. The researcher can only make one claim on either the null hypothesis or the alternative hypothesis in the traditional method of hypothesis testing.
2. If the sample value fall in the critical region, the alternative hypothesis is rejected.
3. Rejecting the null hypothesis will direct the researcher to state the alternative hypothesis.
4. If a sample mean is in the critical region with α = 0.05, it would still be in the critical region even if the alpha was changed to α = 0.01.
5. If a researcher obtains a test score of z = 2.5 for a hypothesis test using α = 0.01, then the researcher should reject the null hypothesis for a right-tailed test, however, the researcher should not reject the null hypothesis for a two-tailed test.
6. A confidence interval is a range of values used to estimate the true value of a sample statistic.

The number of people looking to change auto insurance companies reached a record low. However, for the population of those people who were looking for a better deal, 45% did change companies. Suppose 110 people looking for a better deal on auto insurance are selected at random and the number who actually switch policies is determined. Find the probability that the sample proportion will be between 0.37 and 0.47.

Trevor Harty , an avid mountain biker always wanted to start a business selling top of the line mountain bikes and other outdoor supplies , A little over 6 yearv ago , he and a silent partner opened  a store called Hale and Harty Trail bikes and supplies. Growth was rapid in the first 2 yeard, but since that time , growth in sales has slowed a bit , as expressed , The quarterly sales in ( $1000) for past 4 years.

Year1 year2 year3 year4

274  282     282      296

172   178      182       210

130    136     134      158

16    168.      170       182

(a) Develop atrend using data ,Use this to forecast sales for each quarter of year 5.What doess slope of the line indicates?

(b) use the multiplicative decompostion model to incorporate both trend and seasonal components into the forecast, What does the slope of this line indicate ?

Compare the slope of trend line in part(a) to the slope in the trend line for decomposition for trend that based on deseasonalized sales figure , Discuss why thes are so different and explain which one is best route?

1). There are three insurance companies in the Business District in Accra. It is known from previous records that each year, 2 percent, 5 percent and 3 percent of those insured by Vanguard Insurance, Enterprise Insurance and Star insurance respectively submit claims. 20 percent of the people in the community have an insurance policy with Vanguard Insurance Company, 30 percent with Enterprise Insurance Company and 50 percent with Star Insurance Company.

(i) What is the probability that a randomly selected insurance policyholder in the community did a claim in a certain year?

(ii) If a randomly selected policy holder in the community is found to have made a claim in a certain year, what is the probability that, that person is insured with Vanguard Insurance?

(iii) If a randomly selected policy holder in the community is found to have made a claim in a certain year, what is the probability that, that person is insured with Enterprise Insurance?

2 (a). Researchers are concerned about the impact of students working while they are enrolled in classes, and they’d like to know if students work too much and therefore are spending less time on their classes than they should be. First, the researchers need to find out, on average, how many hours a week students are working.

They know from previous studies that the standard deviation of this variable is about 5 hours.

(i) A survey of 200 students provides a sample mean of 7.10 hours worked. 95% confidence interval based on this sample is 6.41 to 7.79. Do you agreed with the researcher that the 95% confident interval of the unknown population mean of the students worked hours lies between 6.41 and 7.79? Indicate whether the researchers are right or wrong, giving reasons for your answer.

(ii) Based on your understanding of confident interval estimation; explain the reason why the researcher did not use 100% confidence level, but instead, he used 95% confidence level.

(iii) The researchers are not satisfied with their confidence interval and want to do another study to find a shorter confidence interval. What should they change to ensure they find a shorter confidence interval?

3) The average lifespan of a Ghanaian is 57years. The average lifespan of males in Ghana is known to be 55 years while the average lifespan of females in Ghana is known to be 60 years. The average lifespan of people from the Northern region of Ghana is known to be 58 years while the average lifespan of people in the East region of Ghana is known to be 54 years. Use the above information to answer the following questions:

(I). With your reasons, discuss all possible population parameters from the above information.

(ii). With your reasons, discuss all possible sample statistics from the above information.

(iii) Compare and contrast the average lifespan of males and CR(10marks) 4 females. Which group average is more likely to represent the corresponding population parameter? Give reasons for your answer.

4) In each of the following research situations below, determine whether the data should be analyzed with a parametric test, a nonparametric test, or both. Give reasons for your answer in each situation.

(i). You want to compare males and females scores obtained from an aptitude test where scores on the aptitude test range between 0 and 100.

(ii). You want to find out whether or not basketball players are taller than the general population.

(iii). You want to find out whether or not a difference exists between males and females in their like or dislike for statistics.

(iv). You want to find out among a sample of eligible voters in the Ghanaian population, whether the political party they voted for in the 2016 general elections was the same as the political party they voted for in the 2012 general elections.

(v).You want to compare two groups of university students on their levels of intelligence, where intelligence scores could range between 30 and 150