1. For the z -score formula as it is used in a hypothesis test, answer the follo

Question

1. For the z-score formula as it is used in a hypothesis test, answer the following questions.

(a) Explain what is measured by M - in the numerator.

M - measures the difference between the sample mean and the hypothesized population mean.

M - measures the difference between the sample mean and the standard error.    

M - measures the difference between the sample mean and sample standard deviation.

M - measures the difference between hypothesized population mean and the sample standard deviation.

(b) Explain what is measured by the standard error in the denominator.

This measures how much difference, on average, is reasonable to expect between M and .

This measures how much difference, on average, is reasonable to expect between and .    

This measures how much difference, on average, is reasonable to expect between M and .

This measures the variance of the z-scores.

2. Answer the following questions.

(a) What happens to the boundaries for the critical region when the alpha level is changed from = .05 to = .01?

more extreme

less extreme    

remain constant

(b) What happens to the probability of a Type I error when the alpha level is changed from = .05 to = .01?

increase

decrease    

remain constant

3. Although there is a popular belief that herbal remedies such as Ginkgo biloba and Ginseng may improve learning and memory in healthy adults, these effects are usually not supported by well-controlled research. In a typical study, a researcher obtains a sample of n = 16 participants and has each person take the herbal supplements every day for 90 days. At the end of the 90 days, each person takes a standardized memory test. For the general population, scores from the test are normally distributed with a mean of = 80 and a standard deviation of = 21. The sample of research participants had an average of M = 83.

(a) In a sentence, state the null hypothesis being tested.

The herbal supplements have no effect on memory scores.

The herbal supplements have an increasing effect on memory scores.    

The herbal supplements have a decreasing effect on memory scores.

(b) Using symbols, state the null hypothesis and the alternative hypothesis.

H0: = 80; H1: < 80

H0: = 83; H1: 83    

H0: = 80; H1: > 80

H0: = 80; H1: 80

(c) Conduct the hypothesis test using a two-tailed test with = 0.05. (Round your answers to two decimal places.)

z-critical = +-

z=

Conclusion

Fail to reject the null hypothesis. The herbal supplements do not have a significant effect on memory scores.

Reject the null hypothesis. The herbal supplements have a significant effect on memory scores.    

Fail to reject the null hypothesis. The herbal supplements have a significant effect on memory scores.

Reject the null hypothesis. The herbal supplements do not have a significant effect on memory scores.

4. A researcher is testing the effectiveness of a new drug that is intended to improve learning and memory performance. A sample of n = 16 rats is obtained, and the rats are administered the drug and then are tested on a standardized learning task. For the general population of rats (with no drug) the average score on the standardized task is = 50 with a standard deviation of = 10. The distribution of test scores is normal.

If the drug has a 4-point effect and produces a mean score of M = 54 for the sample, is this sufficient to conclude that there is a significant effect using a two-tailed test with = .05? (Use 2 decimal places.)

z-critical = +-

z =

Conclusion

Fail to reject the null hypothesis, there is not a significant effect.

Fail to reject the null hypothesis, there is a significant effect.    

Reject the null hypothesis, there is not a significant effect.

Reject the null hypothesis, there is a significant effect.

If there is a 6-point effect with a sample mean of M = 56, is this sufficient to conclude that there is a significant effect using a two-tailed test with = .05? (Use 2 decimal places.)

z-critical = +-

z =

Conclusion

Fail to reject the null hypothesis, there is a significant effect.

Reject the null hypothesis, there is not a significant effect.    

Fail to reject the null hypothesis, there is not a significant effect.

Reject the null hypothesis, there is a significant effect.

Explanation / Answer

1) A)

U = AVERAGE MEAN (SAMPLE)

M = MEAN OF THE SAMPLE(POPULATION , HYPOTHESISED)

THEREFORE M-U = DIFFERENCE BETWEEN THE MEAN OF THE SAMPLE AND THE POPULATION'HENCE OPTION A IS CORRECT

B)SAMPLE MEAN DEVIATION FROM THE MEAN IN ACTUAL IS KNOWN AS STANDARD ERROR.

THEREFORE OPTION C IS CORRECT,

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