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Chapter 10: Q. 32 (page 626)

In an experiment to learn whether Substance M can help restore memory, the brains of 20rats were treated to damage their memories. The rats were trained to run a maze. After a day, 10rats (determined at random) were given M and 7of them succeeded in the maze. Only 2of the 10control rats were successful. The two-sample z test for 鈥渘o difference鈥� against 鈥渁 significantly higher proportion of the M group succeeds鈥�

(a) gives z=2.25,P<0.02

(b) gives z=2.60,P<0.005

(c) gives z=2.25,P<0.04but not <0.02

(d) should not be used because the Random condition is violated

(e) should not be used because the Normal condition is violated.

Short Answer

Expert verified

The two-sample z test for 鈥渘o difference鈥� against 鈥渁 significantly higher proportion of the M group succeeds鈥� option (e) should not be used because the Normal condition is violated.

Step by step solution

01

Given information

The treated rats to damage their memories =20

Number of rats given M =10

Succeeded rats in maze=7

successful rats=2

02

Explanation

To achieve the Normal requirement, the number of failures in the number of successes in both samples must be greater than 10.

The Normal criterion is not met because there are 7successes in the first sample and 2successes in the second sample.

As a result, it shouldn't be used because the Normal condition has been broken.

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Most popular questions from this chapter

A large toy company introduces a lot of new toys to its product line each year. The company wants to predict the demand as measured by y, first-year sales (in millions of dollars) using x, awareness of the product (as measured by the proportion of customers who had heard of the product by the end of the second month after its introduction). A random sample of 65new products was taken, and a correlation of 0.96was computed. Which of the following is a correct interpretation of this value?

(a) Ninety-six percent of the time, the least-squares regression line accurately predicts first-year sales.

(b) About 92%of the time, the proportion of people who have heard of the product by the end of the second month will correctly predict first-year sales.

(c) About 92%of first-year sales can be explained by the proportion of people who have heard of the product by the end of the second month.

(d) The least-squares regression line relating the proportion of people who have heard of the product by the end of the second month and first-year sales will have a slope of 0.96.

(e) Ninety-two percent of the variation in first-year sales can be explained by the least-squares regression line with proportion of people who have heard of the product by the end of the second month as the explanatory variable.

Dropping out You have data from interviews with a random sample of students who failed to graduate from a particular college in 7years and also from a random sample of students who entered at the same time and did graduate. You will use these data to compare the percentages of students from rural backgrounds among dropouts and graduates.

The correlation between the heights of fathers and the heights of their (grownup) sons isr=0.52 , both measured in inches. If fathers鈥� heights were measured in feet and sons鈥� heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be

(a) much smaller than 0.52.

(b) slightly smaller than 0.52.

(c) unchanged; equal to 0.52.

(d) slightly larger than 0.52.

(e) much larger than 0.52.

Did the treatment have an effect? The investigators expected the control group to adjust their breeding date the next year, whereas the well-fed supplemented group had no reason to change. The report continues: "But in the following year, food-supplemented females were more out of synchrony with the caterpillar peak than the controls." Here are the data (days behind caterpillar peak):

Carry out an appropriate test and show that it leads to the quoted conclusion.

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.
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