The data set below contains the electricity​ costs, in​ dollars, during July 2013 for a random sample of

30 ​one-bedroom apartments in a large city. Complete parts​ (a) and​ (b).

a. Decide whether the data appear to be approximately normally distributed by comparing data characteristics to theoretical properties.

A.​No, the mean and median of the data are too different for the distribution to be normal.

B.No, the range of the data is too great for the distribution to be normal.

C.Yes, the distribution of the data appears to closely resemble a normal distribution.

D.No, the interquartile range of the data is too small for the distribution to be normal

B) Decide whether the data appear to be approximately normally distributed by constructing a normal probability plot.

Design an experiment in which you would perform some sort of hypothesis test about frequencies. For your chosen experiment, explain your entire experimental design. What is your population of interest? How are you going to randomly sample the pop? How many replicates will you collect? What will be the form of the data you collect and what test will you perform? What is your null and alternative hypothesis?

Kolkmeyer Manufacturing Company is considering adding two machines to its manufacturing operation. This addition will bring the number of machines to ten. The president of Kolkmeyer asked for a study of the need to add a second employee to the repair operation. The arrival rate is 0.05 machines per hour for each machine, and the service rate for each individual assigned to the repair operation is 0.4 machines per hour.

1. Compute the operating characteristics if the company retains the single-employee repair operation. If required, round your answers to four decimal places.
   

   	P0	=
   	Lq	=
   	L	=
   	Wq	=  hours
   	W	=  hours

2. Compute the operating characteristics if a second employee is added to the machine repair operation. If required, round your answers to four decimal places.
   

   	P0	=
   	Lq	=
   	L	=
   	Wq	=  hours
   	W	=  hours

3. Each employee is paid $25 per hour. Machine downtime is valued at $75 per hour. From an economic point of view, should one or two employees handle the machine repair operation? Explain. If required, round your answers to two decimal places.
   
   Cost of one employee system: $  
   
   Cost of two employees system: $  
   
   From an economic point of view, two employees  should handle the machine repair operation.

(PLEASE TYPE THE ANSWERS) (STATISTICS 500)

In a large clinical​ trial, 390 comma 827390,827 children were randomly assigned to two groups. The treatment group consisted of 194 comma 857194,857 children given a vaccine for a certain​disease, and 3030 of those children developed the disease. The other 195 comma 970195,970 children were given a​ placebo, and 9494 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Complete parts​ (a) through​ (d) below

a. Assume that a

0.050.05

significance level will be used to test the claim that

p 1p1less than<p 2p2.

Which is​ better: A hypothesis test or a confidence​ interval?

▼

A confidence interval

A hypothesis test

is better.

b. In​ general, when dealing with inferences for two population​ proportions, which two of the following are​ equivalent: confidence interval​ method; P-value​ method; critical value​ method?

▼

Confidence interval method and critical value methodConfidence interval method and critical value method

Confidence interval method and Upper P dash value methodConfidence interval method and P-value method

Upper P dash value method and critical value methodP-value method and critical value method

are​ equivalent, in that they will always lead to the same conclusion. Both of these methods use a standard deviation based on

▼

estimated values of the population proportions,

the assumption that the two population proportions are equal,

whereas the other method uses a standard deviation based on

▼

the assumption that the two population proportions are equal.

estimated values of the population proportions.

c. If a

0.050.05

significance level is to be used to test the claim that

p 1p1less than<p 2p2​,

what confidence level should be​ used?

nothing​%

​(Type an integer or a​ decimal.)

d. If the claim in part​ (c) is tested using this sample​ data, we get this confidence​ interval:

negative 0.000419−0.000419less than<p 1p1minus−p 2p2less than<negative 0.000232−0.000232.

What does this confidence interval suggest about the​ claim?

Because the confidence interval

▼

does not contain

contains

▼

0,

the critical value,

the significance level,

the pooled sample proportion,

there

▼

appears to be

does not appear to be

a significant difference between the two proportions. Because the confidence interval consists

▼

only of values less than

only of values greater than

of values both less than and greater than

▼

0,

the pooled sample proportion,

the significance level,

the critical value,

it appears that the first proportion is

▼

less than

greater than

not significantly different from

the second proportion. There is

▼

insufficient

sufficient

evidence to support the claim that the rate of polio is less for children given the vaccine than it is for children given a placebo.

Confounding

Problem 17

In the popular TV cartoon series, "The Simpsons," the Simpson family has five members: Homer, Marge, Bart, Lisa, and Maggie. Let's involve the Simpsons in Simpson's Paradox.

Consider Homer and Bart's consumption of potato chips and donuts. Suppose that Marge is in the room 20% of the time that Bart is eating chips and 50% of the time that Bart is eating donuts. Similarly, suppose that Marge is in the room 20% of the time that Homer is eating chips and 50% of the time that Homer is eating donuts; thus she catches them eating each kind of snack equally often. Nonetheless, Marge is in the room 32% of the time that Bart is eating either donuts or chips, and Marge is in the room 41% of the time that Homer is eating either donuts or chips. Suppose that Homer and Bart never eat chips and donuts in the same snack--eating chips and eating donuts are mutually exclusive.

a) What fraction of the time that Bart eats either chips or donuts does he eat donuts? ______

b) What fraction of the time that Homer eats either chips or donuts does he eat donuts? ______

In a simple random sample of 100 households, the sample mean number of personal computers was 1.32. Assume the population standard deviation is 0.41. Construct a 95% confidence interval for the mean number of personal computers.

(a) (1.24, 1.40)

(b) (1.25, 1.39)

(c) (0.15, 0.67)

(d) (0.19, 0.63)

Assume that the average volume of raindrops globally is normally distributed with mean 0.45 ml and variance 0.01 ml². Michael measures the volume of two raindrop at Rainyville as 0.65 ml and 0.75 ml; and comes to believe that the raindrops at Rainyville are significantly larger than the global average at the 5% level.

If Michael performs the appropriate statistical test, what will be his conclusion?

1. reject the null hypothesis or 2. fail to reject the null hypothesis?

(A) Suppose two coin are tossed, determine the sample space and find two sigma field over the sample. (B) From the experiment also give example of a set that is not a sigma field (C) With examples, define and explain in details the concept of (a) Probability space (b) Probability Measure (c) sigma algebra or sigma field

Burping (also known as "belching" or "eructation") is one way the human body expels excess gas in your digestive system. It occurs when your stomach fills with air, which can be caused by swallowing food and liquids. Drinking carbonated beverages, such as soda, is known to increase burping because its bubbles have tiny amounts of carbon dioxide in them.

As an avid soda drinker and statistics student, you notice you tend to burp more after drinking root beer than you do after drinking cola. You decide to determine whether there is a difference between the number of burps while drinking a root beer and while drinking a cola. To determine this, you select 20 students at random from high school, have each drink both types of beverages, and record the number of burps. You randomize which beverage each participant drinks first by flipping a coin. Both beverages contain 12 fluid ounces. Here are the results:

Part A: Based on these results, what should you report about the difference between the number of burps from drinking root beer and those from drinking cola? Give appropriate statistical evidence to support your response at the α = 0.05 significance level.

Part B: How much of a difference is there when an individual burps from drinking root beer than from drinking cola? Construct and interpret a 95% confidence interval.

Part C: Describe the conclusions about the difference between the mean number of burps that might be drawn from the interval. How do they relate to your conclusion in part A?

Provided below are summary statistics for independent simple random samples from two populations. Use the pooled​ t-test and the pooled​ t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.

x1= 18, s1= 4, n1= 21, x2= 21, s2= 5, n2=13

a. What are the correct hypotheses for a​ left-tailed test?

b. Compute the test statistic

. c. Determine the​ P-value. d.

The 90% confidence interval is from _____ to _______ ?

Given the following relationship:

Shoe Size | Height (inches)

7.5 66

8 67

8 68

10 71

10.5 70

11 73

a) Letting the variable x represent shoe size and y represent height, determine the least squares regression line and correlation coefficent.

b) Based on the correlation coefficient calculated above, can the least squares regression line be confidently used as a predictor of height? Why or Why not?

Please help show work.

A survey of daily travel time had these results (in minutes):

26, 33, 65, 28, 34, 55, 25, 44, 50, 36, 26, 37, 43, 62, 35, 38, 45, 32, 28, 34

The Mean is 38.8 minutes, and the Standard Deviation is 11.4 minutes

• Identify the data values that represent the middle 68% of the normal curve
• Identify the data values that represent the middle 95% of the normal curve
• Identify the data values that represent the middle 99.7% of the normal curve

Allstate Batteries advertises and sells a 4 year (48 months) battery. You work at Consumer Digest, a consumer advocacy organization, and have been receiving complaints from consumers who felt they were not receiving their full 48 months. Test Allstate’s claim that these are 48 month batteries at the 5% level of significance. You have tested a sample of 36 cars and found a mean of 45months and a standard deviation of 1 month. State the appropriate hypotheses from the consumers’ point of view, show drawing and appropriate critical value, compute the appropriate test statistic, accept(fail to reject)/reject the null hypothesis and draw conclusion. Do you believe the batteries are as advertised? Construct a 99% confidence interval for the unknown mean.

H :

H :

18. With statistical power of 95%, the researcher knows that in general
(a) the chance that the alternative hypothesis is true is 95%
(b) the P-value for the study will be 5%
(c) the chance that the null hypothesis is false is 5%
(d) there is a 95% chance that H0 will be rejected if it is not true.

19. A z-score indicates how many standard deviations a value is above or below the mean.
(a) True (b) False

Use for questions 20 - 22. The U.S. Fish and Wildlife Service reported that the mean length of
six-year-old rainbow trout in the Arolik River in Alaska is 441 millimeters with a standard deviation
of 81 millimeters. Assume these lengths are normally distributed.
20. What is the probability the length of a six-year-old rainbow trout is less than 400?
(a) 0.51 (b) 0.3050 (c) 0.6950 (d) -0.51

21. What is the probability the mean length of 30 six-year-old rainbow trout is less than 400?
(a) 0.3050 (b) 0.9972 (c) 0.0028 (d) 0.6950

22. What is the length of a six-year-old rainbow trout that is at the 80th percentile?
(a) 457.20 (b) 505.80 (c) 372.96 (d) 509.04

23. A psychologist is concerned about the health of veterans returning from war. She examines 20 veterans
and assesses whether they show signs of post-traumatic stress disorder. What is the sample of interest?
(a) All veterans returning from war. (b) The 20 veterans examined.
(c) All psychologists. (d) Veterans with post-traumatic stress disorder.

24. Is the underlined value a parameter or statistic? In a recent poll, 57% of the respondents supported a
school bond issue.
(a) Statistic (b) Parameter

25. According to the Internal Revenue Service, the proportion of federal tax returns for which no tax was
paid was 32.6%. As part of a tax audit, tax officials draw a simple random sample of 120 tax returns.
What is the probability that the sample proportion of tax returns for which no tax was paid is greater
than 40%?
(a) 0.0418 (b) 0.0495 (c) 0.9505 (d) 0.9582

The IMF is an international organization of 189-member countries that, among other things, looks to assist nations that can’t pay their international debt obligations.

Assume that a financial analyst for the IMF was reading the study “Analysis and Modeling of Recent Business Failures in Greece,” in Managerial and Decisions Economics (1992). In this study, the authors compared various characteristics of firms that failed against firms that succeeded. One of the variables studied was the Current Ratio of firms. This is a measure of liquidity that measures the ratio of Current Assets to Current Liabilities. Generally speaking, the Current Ratio of a company is roughly the amount a firm is worth divided by what it owes. For a sample of 68 firms that succeeded, the average Current Ratio was 1.73 with a standard deviation of .64. For a sample of 33 firms that failed, the average Current Ratio was .82 with a standard deviation of .48. At the 5% level of significance, test the hypothesis that the Current Ratio of successful firms is significantly greater than that of unsuccessful firms.

A. since the t-score of 7.2 is greater than the critical t-score of 1.66, we reject the null hypothesis that the current ratio of successful firms is less than or equal to that of unsuccessful firms. There is some evidence to suggest that the current ratio of successful firms might be greater than that of unsuccessful firms.

B. since the t-score of 7.2 is greater than the critical t-score of 1.66, we cannot reject the null hypothesis that the current ratio of successful firms is less than or equal to that of unsuccessful firms. There is some evidence to suggest that the current ratio of successful firms might be greater than that of unsuccessful firms.

C. since the t-score of 7.2 is greater than the critical t-score of 1.66, we reject the null hypothesis that the current ratio of successful firms greater than or equal to that of unsuccessful firms. There is some evidence to suggest that the current ratio of successful firms might be less than that of unsuccessful firms.

D. since the t-score of 7.2 is greater than the critical t-score of 1.66, we cannot reject the null hypothesis that the current ratio of successful firms is greater or equal to that of unsuccessful firms. There is some evidence to suggest that the current ratio of successful firms might be greater than that of unsuccessful firms. <br>e, none of these answers are correct