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A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of u = 80 and a standard deviation of o = 20. The researcher expects a 12-point treatment effect and plans to use a two-tailed hypothesis test with a .05.

a. Compute the power of the test if the researcher uses a sample of n = 16 individuals. (See Example 8.6.)

b. Compute the power of the test if the researcher uses a sample of n = 25 individuals

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

Costco Customer Satisfaction. Consumer Reports uses a 100-point customer satisfaction score to rate the nation's major chain stores. Assume that from past experience with the satisfaction rating score, a population standard deviation of is expected. In 2012, Costco, with its 432 warehouses in 40 states, was the only chain store to earn an outstanding rating for overall quality. A sample of 15 Cosco customer satisfaction scores follows.

95   90   83   75   95   98   80   83   82   93   86   80   94   64   62

a. What is the sample mean customer satisfaction score for Costco?

b. What is the sample variance?

c. What is the sample standard deviation?

Construct a hypothesis test to determine whether the population standard deviation of should be rejected for Costco. With a.05 level of significance, what is your conclusion?

 

 A leading magazine (link Barron's) reported at one time that the average number of weeks an individual is unemployed is 29 weeks. Assume that the length of unemployment is normally distributed with a population mean of 29 weeks and the population standard derivation of 4 weeks. Suppose you would like to select a random sample of 16 unemployed individuals for a follow-up study. Round the answers of the following questions to 4 decimal places.

1. What is the distribution of XX? XX-N(,)

2. What is the distribution of "xx"? "xx"-N(,)

3. What is the probability that one randomly selected individual found a job for more than 27 weeks?

Use the following scenario for questions 6 – 8. In 2016-17, the average SAT score of the UVA first year class was 1420 out of 1600. An advisor in the statistics department is interested in determining whether statistics majors from that class have higher SAT scores than the average. He tests H,:µ = 1420 against Hạ: µ > 1420, where u is the mean SAT score for statistics majors from the 2016-17 first year class. In a simple random sample of 30 statistics majors, he finds a sample mean SAT score of 1440 with sample standard deviation of 40.

6. What is the value of the test statistic for this significance test?

a. 0.09

b. 0.5

c. 2.73

d. 20

7. From what distribution is this test statistic?

a. N(0, 1)

b. N(1420, 7.30)

c. t distribution with 29 degrees of freedom

d. t distribution with 28 degrees of freedom

8.) The p-value for this test is 0.005. Which of the following is a proper interpretation of this p- value?

a.There is a 0.5% chance that the null hypothesis is true.

b. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample a. mean SAT score from 30 statistics majors would equal 1440.

c.If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or lower.

d. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or higher.

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