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Chapter 10: Q. 42 (page 653)

42. Long words Mary was interested in comparing the mean word length in articles from a medical journal and an airline鈥檚 in-flight magazine. She counted the number of letters in the first 200 words of an article in
the medical journal and in the first 100 words of an article in the airline magazine. Mary then used Minitab statistical software to produce the histograms shown.

Short Answer

Expert verified

The random requirement was not met.

Step by step solution

01

Given information

Mary counted the number of letters in the first 200 words of an article in
the medical journal and in the first 100 words of an article in the airline magazine.

02

Explanation

Determine the Random, Normal, and Independent are the requirements from the given histogram:

Random, Normal, and Independent are the requirements for two-samplet methods.
The samples of words were conveniently chosen as the first 200words, which are not representative of all words, hence the Random requirement was not met.

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Most popular questions from this chapter

A fast-food restaurant uses an automated filling machine to pour its soft drinks. The machine has different settings for small, medium, and large drink cups. According to the machine鈥檚 manufacturer, when the large setting is chosen, the amount of liquid dispensed by the machine follows a Normal distribution with mean 27ounces and standard deviation 0.8ounces. When the medium setting is chosen, the amount of liquid dispensed follows a Normal distribution with mean 17ounces and standard deviation 0.5ounces. To test the manufacturer鈥檚 claim, the restaurant manager measures the amount of liquid in a random sample of 25cups filled with the medium setting and a separate random sample of 20 cups filled with the large setting. Let x1-x炉2be the difference in the sample mean amount of liquid under the two settings (large 鈥� medium). Find the probability thatx炉1-x炉2 is more than 12 ounces. Show your work.

鈥淲ould you marry a person from a lower social class than your own?鈥� Researchers asked this question of a random sample of 385black, never married students at two historically black colleges in the South. Of the 149men in the sample, 91said 鈥淵es.鈥� Among the 236women, 117said 鈥淵es.鈥�14Is there reason to think that different proportions of men and women in this student population would be willing to marry beneath their class?

Holly carried out the significance test shown below to answer this question. Unfortunately, she made some mistakes along the way. Identify as many mistakes as you can, and tell how to correct each one.

State: I want to perform a test of

H0:p1=p2

Ha:p1鈮�p2

at the 95%confidence level.

Plan: If conditions are met, I鈥檒l do a one-sample ztest for comparing two proportions.

  • Random The data came from a random sample of 385 black, never-married students.
  • Normal One student鈥檚 answer to the question should have no relationship to another student鈥檚 answer.
  • Independent The counts of successes and failures in the two groups鈥�91,58,117, and 119鈥�are all at least 10

Do: From the data, p^1=91149=0.61and p^2=117236=0.46.

Test statistic

z=(0.61-0.46)-00.61(0.39)149+0.46(0.54)236=2.91

p=value From Table A, role="math" localid="1650292307192" P(z鈮�2.91)鈮�1-0.3982鈮�0.0018.

Conclude: The p-value, 0.0018, is less than 0.05, so I鈥檒l reject the null hypothesis. This proves that a higher proportion of men than women are willing to marry someone from a social class lower than their own.

Computer gaming Do experienced computer game players earn higher scores when they play with someone present to cheer them on or when they play alone? Fifty teenagers who are experienced at playing a particular computer game have volunteered for a study . We randomly assign 25of them to play the game alone and the other 25to play the game with a supporter present. Each player鈥檚 score is recorded.

(a) Is this a problem with comparing means or comparing proportions? Explain.

(b) What type of study design is being used to produce data?

Preventing drowning Drowning in bathtubs is a major cause of death in children less than 5 years old. A random sample of parents was asked many questions related to bathtub safety. Overall, 85% of the sample said they used baby bathtubs for infants. Estimate the percent of all parents of young children who use baby bathtubs.

Mrs. Woods and Mrs. Bryan are avid vegetable gardeners. They use different fertilizers, and each claims that hers is the best fertilizer to use when growing tomatoes. Both agree to do a study using the weight of their tomatoes as the response variable. They had each planted the same varieties of tomatoes on the same day and fertilized the plants on the same schedule throughout the growing season. At harvest time, they each randomly select 15tomatoes from their respective gardens and weigh them. After performing a two-sample t-test on the difference in mean weights of tomatoes, they get t=5.24and P=0.0008. Can the gardener with the larger mean claim that her fertilizer caused her tomatoes to be heavier?

(a) No, because the soil conditions in the two gardens is a potential confounding variable.

(b) No, because there was no replication.

(c) Yes, because a different fertilizer was used on each garden.

(d) Yes, because random samples were taken from each garden.
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