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Do you have ESP? A researcher looking for evidence of extrasensory perception (ESP) tests 500 subjects. Four of these subjects do significantly better (P<0.01) than random guessing.

a. Is it proper to conclude that these four people have ESP? Explain your answer.

b. What should the researcher now do to test whether any of these four subjects have ESP?

Short Answer

Expert verified

Part (a) It is possible that 4 of the 500 subjects have a p-value below the 0.01

Part (b) Researchers should retest these 4 subjects for ESP

Step by step solution

01

Part (a) Step 1: Given information

n=500x=4P<0.01

02

Part (a) Step 2: Calculation

No, since a p-value of 0.01 would be expected in around 1% of the 500subjects Because 1% of 500 subjects corresponds to 5 subjects, it's likely that four of the 500 subjects have a p-value of less than 0.01

When null hypotheses of random guessing are true, the p-value is really the probability of getting test findings, or more extreme, when null hypotheses of random guessing are true. As a result, it's likely that these four participants with p-values less than 0.01did not have EPSP.

Thus, it is possible that 4 of the 500 subjects have a p-value below the 0.01

03

Part (b) Step 1: Calculation

These four subjects should be retested for ESP. If they perform much better than random guessing once more, they are highly likely to have ESP.

Thus, Researchers should retest these 4 subjects for ESP.

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Most popular questions from this chapter

Do you Tweet? The Pew Internet and American Life Project asked a random sample of U.S. adults, 鈥淒o you ever 鈥 use Twitter or another service to share updates about yourself or to see updates about others?鈥 According to Pew, the resulting 95% confidence interval is (0.123, 0.177).11 Based on the confidence interval, is there convincing evidence that the true proportion of U.S. adults who would say they use Twitter or another service to share updates differs from 0.17? Explain your reasoning.

Powerful potatoes Refer to Exercise 85. Determine if each of the following

changes would increase or decrease the power of the test. Explain your answers.

a. Change the significance level to =0.10

b. Take a random sample of 250 potatoes instead of 500 potatoes.

c. The true proportion is p=0.10 instead of p=0.11

Significance tests A test of H0:p=0.65 against Ha:p<0.65

based on a sample of size 400 yields the standardized test statistic z=1.78 .

a. Find and interpret the P-value.

b. What conclusion would you make at the =0.10 significance level? Would

your conclusion change if you used =0.05 instead? Explain your reasoning.

c. Determine the value of p= the sample proportion of successes.

Which of choices (a) through (d) is not a condition for performing a significance test about a population proportion p?

a. The data should come from a random sample from the population of interest.

b. Both np0and n(1-p0)should be at least 10.

c. If you are sampling without replacement from a finite population, then you should sample less than 10%of the population.

d. The population distribution should be approximately Normal unless the sample size is large.

e. All of the above are conditions for performing a significance test about a population proportion.

Potato power problems Refer to Exercises 85 and 87

a. Explain one disadvantage of using =0.10 instead of =0.05 when

performing the test.

b. Explain one disadvantage of taking a random sample of 500 potatoes instead of 250 potatoes from the shipment.

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