4: A researcher is testing how effective a new drug is at improving cognitive skills. A sample of n= 16 participants is obtained, and they are administered the drug. They are then tested on a cognitive task. For the general population (with no drug) the average score on this task is u = 50 with o = normal, and they predict that the drug will increase scores on the cognitive task in the population and set their alpha at a = .05. 10. The distribution is Draw the distribution of sample means where Ho is true and indicate where the critical value is, and whethe it is a z-score or a t-statistic:

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standard deviation
we make about the effectiveness of the new writing program? Assume a 2-tailed test with a = .05.
3c. If the writing scores have a population standard deviation of o = 20, what conclusion should
we make about the effectiveness of the new writing program? Assume a 2-tailed test with a = .05.
3d. Briefly explain why you reached a different conclusion in 3a and 3b.
4: A researcher is testing how effective a new drug is at improving cognitive skills. A sample of n = 16
participants is obtained, and they are administered the drug. They are then tested on a cognitive task. For
the general population (with no drug) the average score on this task is u = 50 with o = 10. The distribution is
normal, and they predict that the drug will increase scores on the cognitive task in the population and set
their alpha at a = .05.
Draw the distribution of sample means where Ho is true and indicate where the critical value is, and whether
it is a 7-score or a t-statistic:
If the sample mean after the drug is M = 56 on the task, is this sufficient to reject Ho ?
5: A random sample of n= 16 individuals is selected from a population with u =70 and a treatment is
administered to everyone in the sample. After treatment, the sample mean is M = 76 with SS = 960. What is
the estimated standard error for the distribution of sample means where Ho is true? (HINT: calculate the
%3D
%3D
sample variance and sample standard deviation first!)
Transcribed Image Text:standard deviation we make about the effectiveness of the new writing program? Assume a 2-tailed test with a = .05. 3c. If the writing scores have a population standard deviation of o = 20, what conclusion should we make about the effectiveness of the new writing program? Assume a 2-tailed test with a = .05. 3d. Briefly explain why you reached a different conclusion in 3a and 3b. 4: A researcher is testing how effective a new drug is at improving cognitive skills. A sample of n = 16 participants is obtained, and they are administered the drug. They are then tested on a cognitive task. For the general population (with no drug) the average score on this task is u = 50 with o = 10. The distribution is normal, and they predict that the drug will increase scores on the cognitive task in the population and set their alpha at a = .05. Draw the distribution of sample means where Ho is true and indicate where the critical value is, and whether it is a 7-score or a t-statistic: If the sample mean after the drug is M = 56 on the task, is this sufficient to reject Ho ? 5: A random sample of n= 16 individuals is selected from a population with u =70 and a treatment is administered to everyone in the sample. After treatment, the sample mean is M = 76 with SS = 960. What is the estimated standard error for the distribution of sample means where Ho is true? (HINT: calculate the %3D %3D sample variance and sample standard deviation first!)
Expert Solution
Step 1

Here, population standard deviation σ is known. Hence it is appropriate to use z-score.

Using Excel formula “=NORM.S.INV(1-(0.05/2))”, the critical value for α = 0.05 is obtained as 1.96.

The distribution of sample means is

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