One of the costs of unexpected inflation is an arbitrary redistribution of purchasing power. Find the loser and winner of the following transactions. In other words, describe how the purchasing power is redistributed with these transactions. b. Jennifer took out a fixed-interest-rate loan from Bank H when the CPI was 100. She expected the CPI to increase to 103 but it actually increased to 105. c. Nick bought some shares of stock and, over the next year, the price per share decreased by 7 percent and the price level decreased by 9 percent. c. Nick bought some shares of stock and, over the next year, the price per share decreased by 7 percent and the price level decreased by 9 percent. d. Jackie saves $100 and receives $106 the next year. During the same year, the price of the basket of goods that she purchases increases from $100 to $104.e. Fifteen years ago T’s parents purchased some land with the idea of selling it later to help pay your college expenses. They purchased the land for $100,000. They sold if for $180,000. During the time they held it the price level rose from 80 to 120.f. One year ago Sam purchased bonds for $100,000. He just sold them for $120,000. During the year the price level rose by 5%.g. Mitch makes payments on a car loan. If the price level a year ago was 120 and people expected it to rise to 125 but it actually rose to 128.

The Decadent Desserts cookbook has recipes for desserts. The number of calories per serving for the recipes in the cookbook is normally distributed with a mean of 378 and a standard deviation of 34.5. If 18 recipes are randomly selected to serve at a reception, what is the probability that the average calories per serving for the sample is over 385?

Assume that females have pulse rates that are normally distributed with a mean of mu equals 73.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts​ (a) through​ (c) below. a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 79 beats per minute. The probability is ____. ​(Round to four decimal places as​ needed.) b. If 4 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 79 beats per minute. The probability is _____. ​(Round to four decimal places as​ needed.) c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30? A. Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size. B. Since the distribution is of​ individuals, not sample​ means, the distribution is a normal distribution for any sample size. C. Since the mean pulse rate exceeds​ 30, the distribution of sample means is a normal distribution for any sample size. D. Since the distribution is of sample​ means, not​ individuals, the distribution is a normal distribution for any sample size.

A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20¢; 75¢; 50¢; 65¢; 30¢; 55¢; 40¢; 40¢; 30¢; 55¢; $1.50; 40¢; 65¢; 40¢. Assume the underlying distribution is approximately normal. You wish to conduct a hypothesis test (α = 0.05 level) to determine if the mean cents off for coupons is less than 50¢.

1. State the null and alternate hypotheses clearly.
2. Conduct the hypothesis test based on the test statistic and critical value(s). Clearly indicate each.
3. What is the p-value? Use the p-value to conduct the same test
4. Report your conclusion in words, in the context of the problem.
5. What is the power of the for an alternative hypothesis value of 49¢?

If x is a binomial random variable, compute P(x) for each of the following cases:

(a)  P(x≤5),n=9,p=0.7P(x≤5),n=9,p=0.7

(b)  P(x>1),n=9,p=0.1P(x>1),n=9,p=0.1

(c)  P(x<3),n=5,p=0.6P(x<3),n=5,p=0.6

(d)  P(x≥1),n=6,p=0.9P(x≥1),n=6,p=0.9

Using the info below, answer the next following questions:

A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20¢; 75¢; 50¢; 65¢; 30¢; 55¢; 40¢; 40¢; 30¢; 55¢; $1.50; 40¢; 65¢; 40¢. Assume the underlying distribution is approximately normal.

(a) Determine the sample mean in cents (Round to 3 decimal places)

(b) Determine the standard deviation from the sample . (Round to 3 decimal places)

(e) Construct a 95% confidence interval for the population mean worth of coupons.  Use a critical value of 2.16 from the t distribution.

What is the lower bound? ( Round to 3 decimal places )

(f)  Construct a 95% confidence interval for the population mean worth of coupons .

What is the upper bound? ( Round to 3 decimal places )

4. (a) In a fraud detection system a number of different algorithms are working indepen- dently to flag a fraudulent event. Each algorithm has probability 0.9 of correctly detecting such an event. The program director wants to be make sure the system can detect a fraud with high probability. You are tasked with finding out how many different algorithms need to be set up to detect a fraudulent event. Solve the following 3 problems and report to the director. [Total: 18 pts] (b) Suppose n is the number of algorithms set up. Derive an expression for the probability that a fraudulent event is detected. (6 pts) (c) Using R, draw a plot of the probability of a fraudulent event being detected versus n, varying n from 1 to 10. (6 pts) (d) Your colleague claims that if the company uses n = 4 algorithms, the probability of detecting the fraudulent event is 0.9999. The director is not convinced. Generate 1 million samples from Binomial distribution with n = 4, p = 0.90 and count the number of cases where Y = 0. Report the number to the director. (6 pts)

Thoroughly answer the following questions:

What is the difference between prevalence and incidence? Provide an example of each. Do not provide the definitions, explain in your own words.

The weights of 22 randomly selected mattresses were found to have a standard deviation of 3.17. Construct the 95% confidence interval for the population standard deviation of the weights of all mattresses in this factory. Round your answers to two decimal places.

1. A social psychologist wanted to determine whether attitudes of men toward abortion were different in rural and urban areas. He prepared a questionnaire and administered it to a group of city dwellers and a group of country dwellers. Each city man was matched with a country man on age, income, and education. High scores indicate positive attitudes towards abortion. The data:

1. What can the social psychologist say about differences in the attitudes of rural and urban men?
2. Justify the statistical method you used to analyze the data.

Nine experts rated two brands of Colombian coffee in a taste-testing experiment. A rating on a 7-point scale ( 1=1= 1 equals extremely unpleasing, 7=7= 7 equals extremely pleasing) is given for each of four characteristics: taste, aroma, richness, and acidity. The following data stored in Coffee contain the ratings accumulated over all four characteristics:

• a. At the 0.05 level of significance, is there evidence of a difference in the mean ratings between the two brands?

• b. What assumption is necessary about the population distribution in order to perform this test?

• c. Determine the p-value in (a) and interpret its meaning.

• d. Construct and interpret a 95% confidence interval estimate of the difference in the mean ratings between the two brands.

SHOW EXCEL FUNCTIONS USED TO ANSWER.

Isabella gathered data on the average percentage of tips received by waitstaff in 31 restaurants in New York City. She works through the testing procedure:

• H0:μ=14%; Ha:μ≠14%
  
• α=0.1 (significance level)
  
• The test statistic is t0=x¯−μ0sn√=1.489.
  
• The critical values are ±t0.05=±1.697.
  

Conclude whether to reject or not reject H0. Select two responses below.

Select all that apply:

• Reject H0.

• Fail to reject H0.

• The test statistic falls within the rejection region.

• The test statistic is not in the rejection region.

2. Set up both the vector of state probabilities and the matrix of transition probabilities given the following information: Store 1 currently has 40% of the market; store 2 currently has 60% of the market. In each period, store 1 customers have an 80% chance of returning; 20% of switching to store 2.

In each period, store 2 customers have a 90% chance of returning; 10% of switching to store 1. a.

Find the percentage of market for each store after 2 periods. b. Find the equilibrium conditions of 2 stores (limiting probabilities). What’s the meaning of these probabilities?

A study of the career paths of hotel general managers sent questionnaires to an SRS of 240 hotels belonging to major U.S. hotel chains. There were 133 responses. The average time these 133 general managers had spent with their current company was 12.37 years. (Take it as known that the standard deviation of time with the company for all general managers is 1.5 years.) (a) Find the margin of error for a 90% confidence interval to estimate the mean time a general manager had spent with their current company: years (b) Find the margin of error for a 99% confidence interval to estimate the mean time a general manager had spent with their current company: years (c) In general, increasing the confidence level the margin of error (width) of the confidence interval. (Enter: ''DECREASES'', ''DOES NOT CHANGE'' or ''INCREASES'', without the quotes.)