What are the z scores and are the sample means unlikely/likely? (Look at photo)

Suppose that a researcher developed a drug that she claims increases extroversion. A sample of n=4 participants has a sample mean of M = 115 on a personality assessment after taking the drug. The personality test has a population mean of = 100 and = 30. 1s the sample mean an especially unlikely result based on the population parameters for the personality test? What if the researcher increased the sample to n m 25 and observes the same sample mean of M=115?

For M = 115 and n = 4 scores:

 

z = _______ which indicates that the sample mean _______ especially unlikely.

 

For M = 115 and n = 25 scores:

 

z = _______ which indicates that the sample mean _______ especially unlikely,

What is the probability of randomly selecting a score less than X = 52?

P(X < 52) =

What is the probability of selecting a random sample of n = 9 scores with a mean less than M = 52?

P(M < 52) =

(Look at photo)

What is the probability of selecting a random sample of n = 16 scores with a mean less than M = 52?

P(M < 52) =

which of the following is not a property of the sampling distribution of the sample​ mean?

A. The expected value of the sample mean is equal to the population mean.

B. The mean of the sample means is the population mean.

C. The distribution of the sample mean tends to be skewed to the right or left.

D. The sample means target the value of the population mean.

In a study with a sample mean of 14, a z of +2.0 is obtained. With a critical value of ± 1.96, the research team decides not to reject the idea that the sample represents a µ of 12.
a. Describe/draw the sampling distribution and indicate the relative locations of 𝑋̅, µ, the
computed z-score, and the two critical values. 
b. Is the conclusion given correct? Explain your answer. 
c. What population is this sample likely to represent?