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Question: to test the effectiveness of a treatment a sample of...

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To test the effectiveness of a treatment, a sample of n = 36 people is selected from a normal population with mean of μ = 60. After the treatment is administered to the individuals in the sample, the sample mean is found to be M = 55.

(a) If the population standard deviation is σ = 13, can you conclude that the treatment has a significant effect? Use a two-tailed test with α = 0.05. (Round your answers to two decimal places.)

z-critical = ±
z =


Conclusion:

a)Reject the null hypothesis, there is a significant treatment effect.

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

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

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


(b) If the population standard deviation is σ = 19, can you conclude that the treatment has a significant effect? Use a two-tailed test with α = 0.05. (Round your answers to two decimal places.)

z-critical = ±
z =


Conclusion

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


(c) Compute Cohen's d to measure effect size for both tests (σ = 13 and σ = 19). (Round your answers to two decimal places.)

σ = 13     d =
σ = 19     d =


(d) Briefly describe how the standard deviation influences the outcome of the hypothesis test. How does σ influence measures of effect size?

A)A larger standard deviation reduces the likelihood of rejecting the null hypothesis, but has no effect on Cohen's d.

B) larger standard deviation reduces the likelihood of rejecting the null hypothesis, but increases effect size.

C)A larger standard deviation reduces the likelihood of rejecting the null hypothesis and reduces effect size.

D)A larger standard deviation increases the likelihood of rejecting the null hypothesis, but reduces effect size.

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