The probability value, or p-value, is an important value generated by a variety of statistical analyses. Select all of the following that are true when considering a p-value: a. The p-value is the probability that both the null hypothesis and the observed data are both true at the same time b. A high p-value, say p = 0.40, means is it highly unlikely that the null hypothesis and the observed data are both true. c. A high p-value, say p = 0.40, means is it highly likely that the null hypothesis and the observed data are both true. ✓d. When the p-value is greater than alpha (p>0.05), we fail to reject the null hypothesis. The observed data do match our expectations. e. When the p-value is less than alpha (p < 0.05), we reject the null hypothesis. The observed data do not match our expectations.

Which of the following is not true about statistical significance?   the difference is a result of random chance.   the result is statistically significant when p-value is less than alpha level.   The probability of a result occurring by chance is less than the alpha level.   the result is statistically significant when we reject the null hypothesis.

Risk analysis and Standard Deviation.Consider the following two games:Game 1: Toss a fair coin once. If it comes up Heads, you win $100. If it comes up tails, you lose nothing--zero dollars.Expected Value or ? = Standard Deviation or ? = There are only two two possible values--$0 or $100 (each with probability 0.5).Game 2: Toss a fair coin a hundred times. For each Heads that comes up, you win $1 and for tails you lose nothing.The amount of dollars is equivalent to the number of Heads that turn up. This can be viewed in terms of Binomial Probabilities, with p = q = 0.5 and n = 100 (See Section 5.3, page 232 of the textbook).Expected Value or ? = Standard Deviation or ? = Standard Deviation measures the "risk" of the two games. Since the Standard Deviation of Game 2 is lower than that of Game 1, Game 2 is "less risky". This can be further analyzed by calculating the usual values in Game 2 (See Section 5.3, page 233 of the textbook. Also Problem 5 on page 237 is relevant.). Here "usual"…

Consider the following example survey results of 18 - to 34 year olds in the United States, in response to the question "Are you currently living with your family?"  Show steps in Excela Develop the joint probability table for the data to the right and use it to answer thefollowing questions.b What are the marginal probabilities c What is the probability of living with family given you are an 18 to 34 year oldman in the U.S.? What is the probability of living with family given you are an 18 to 34 year old woman in the U.S.? What is the probability of an 18 to 34 year old in the U.S. Living with family? If, in the U.S., 49.9% of 18 to 34 year olds are male, do you consider this a goodrepresentative sample? Why?                       Yes           No      Totals Men             106           141        247Women          92           161        253 Totals           198           302        500

Incomes in a certain town are strongly right-skewed with mean $40,000 and standard deviation $8,000. A random sample of 5 households is taken. What is the probability the average of the sample is more than $42,000?

The following table shows the results of a medical test. Positive Test Result Negative Test Result 95.3 4.6 Total 82.6 % 4.6 Has Disease X % 491 24 % 515 Does Not Have Disease 45 Use the preceding data to estimate each of the following. (Express each response as a percentage rounded to one decimal place.) a. If a person has the disease, what is the probability that person tests positive? This is the sensitivity or true positive rate of a test. 214 259 Total b. If a person has the disease, what is the probability that person tests negative? This is sometimes called the false negative rate. 536 238 774 c. If a person does not have the disease, what is the probability that person tests negative? This is the specificity or true negative rate of a test. d. If a person does not have the disease, what is the probability that person tests positive? This is sometimes called the false positive rate. X %

Consider the following hypothetical survey results of 18- to 34-year-olds in a certain country, in response to the question "Are you currently living with your family?"   Yes No Totals Women 94 154 248 Men 108 144 252 Totals 202 298 500 (a) Develop the joint probability table for these data and use it to answer the following questions.   Yes No Totals Women       Men       Totals       (b) What are the marginal probabilities? P(18- to 34-year-old woman) = P(18- to 34-year-old man) = P(responded yes) = P(responded no) = (c) What is the probability of living with family given you are an 18- to 34-year-old woman in this country? (Round your answer to four decimal places.)   (d) What is the probability of living with family given you are an 18- to 34-year-old man in this country? (Round your answer to four decimal places.)   (e) What is the probability of an 18- to 34-year-old in this country living with family?   (f) If, in this country,…

The following table shows the results of a medical test. Positive Test Result Negative Test Result Total % Has Disease % 165 13 % 178 Does Not Have Disease % 28 97 125 Total Use the preceding data to estimate each of the following. (Express each response as a percentage rounded to one decimal place.) 193 a. If a person tests positive, what is the probability that person has the disease? This is sometimes called the PPV (positive predictive value). 110 303 b. If a person tests positive, what is the probability that person does not have the disease? This is sometimes called the false discovery rate. c. If the person tests negative, what is the probability that person does not have the disease? This is sometimes called the NPV (negative predictive value). d. If the person tests negative, what is the probability that person has the disease? This is sometimes called the false omission rate.

True or false