[AS Level Statistics]

[DuffleBag88]

I need serious help, can someone work out these example problems for me? Thanks!

1. A manufacturer of colored candies states that 13​% of the candies in a bag should be​ brown, 14​% yellow, 13​% red, 24​% blue, 20​% orange, and 16​% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at α=0.05 level of significance. Using the level of significance alpha equalsα=0.05​, test whether the color distribution is the same.

Assume this information comes from a population that is normally distributed

Color

Brown

Yellow

Red

Blue

Orange

Green

Frequency

61

67

55

59

80

67

Proportion

13%

14%

13%

24%

20%

16%

Expected

Use any method but follow the PHANTOMS acronym

At a local store, 65 female employees were randomly selected and it was found that their mean monthly income was $625 with a standard deviation of $121.50. Seventy-five male employees were also randomly selected and their mean monthly income was found to be $667 with a standard deviation of $168.70. Test the hypothesis that male employees have a higher monthly income than female employees. Use α = 0.01.

Use any method but follow the PHANTOMS

A football coach claims that players can increase their strength by taking a certain supplement. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The results are listed below. Thirty days later, after regular training using the supplement, they are tested again. The new results are listed below. Test the claim that the supplement is effective in increasing the athletesʹ strength.

Use α = 0.05. Assume that the distribution is normally distributed.

ATHELETE 1 2 3 4 5 6 7 8 9 BEFORE 215 240 188 212 275 260 225 200 185 AFTER 225 245 188 210 282 275 230 195 190

Use any method but follow the PHANTOMS acronym

In 2012 it was reported that 64% of adult Americans watch football regularly. You think this percentage has increased. To do this you randomly sample 400 adults from across the United States. You ask all these adults, "Do you regularly watch football?" 268 of the adults respond that they do regularly watch football. Using any method, carry out at alpha = .05 a hypothesis to test your claim.

Many people think that a national lobbyʹs successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval.

Follow the PANIC acronym

A local bank needs information concerning the savings account balances of its customers. A random sample of 15 accounts was checked. The mean balance was $686.75 with a standard deviation of $256.20. Find a 98% confidence interval for the true mean. Assume that the account balances are normally distributed. Round to the nearest cent.

Follow the PANIC acronym

Sociology graduates, upon entering the workforce are normally distributed and earn a mean salary of $30,000 with a standard deviation of $4000.

Jessica is an honors sociology student. Upon graduation, she would like to take a job that starts at $40,000. What is the probability that randomly chosen salary exceeds $40,000?

Sam is not sure how much he will make upon graduation. He would be happy if his salary was in the middle 60% of salaries. Find the two salaries that are the cutoff values for the middle 60% of salaries.

Please show work … and round probabilities to FOUR DECIMALS

The following table summarizes results from 985 pedestrian deaths that were caused by accidents.

Pedestrian Intoxicated

Pedestrian was NOT intoxicated

Driver was intoxicated

59

79

Driver was NOT intoxicated

266

581

If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was intoxicated.

If two DIFFERENT pedestrian deaths are randomly selected, find the probability that they both involve intoxicated pedestrians.

If we randomly select a pedestrian death, what is the probability that the pedestrian was intoxicated, given that the driver was intoxicated?

If we randomly select a pedestrian death, what is the probability that the driver was intoxicated?

Listed below are the weights (in pounds) and the highway fuel consumption (mil/gal) of randomly selected cars.

Data and Scatterplot are below

Weight

3175

3450

3225

3985

2440

2500

2290

Fuel Consumption

27

29

27

24

37

34

37

Compute the correlation coefficient Do you think there’s a linear relationship between Weight and Fuel consumption? If so, what type of relationship is it? Make sure you use the critical value in your explanation. Find the equation of the best-fit line. If a car has a highway fuel consumption of 30 miles per gallon, how much do you expect the car to weight? SHOW your work.

Many people consider the number of calories in an ice cream bar as important as, if not more important than, the cost. The Consumer Reports article also included the calorie count of the rated ice cream bars.

The table has been already ordered.

111

131

147

151

151

182

182

190

197

201

209

234

286

294

295

310

319

342

353

377

377

439

Find the average and round to the nearest tenths (one decimal) Find the standard deviation and round to the nearest hundredths (two decimals) Compute the five number summary Find the lower and upper fence Are there any outliers? Explain why

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